angles around a point problem solving

Angles Around A Point Worksheet

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Help your students prepare for their Maths GCSE with this free angles around a point worksheet of 44 questions and answers

• Section 1 of the angles around a point worksheet contains 36 skills-based angles around a point questions, in 3 groups to support differentiation
• Section 2 contains 4 applied angles around a point  questions with a mix of worded problems and deeper problem solving questions
• Section 3 contains 4 foundation and higher level GCSE exam style angles around a point questions 
• Answer keys and a mark scheme for all angles around a point questions are provided
• Questions follow variation theory with plenty of opportunities for students to work independently at their own level
• All questions created by fully qualified expert secondary maths teachers
• Suitable for GCSE maths revision for AQA, OCR and Edexcel exam boards
• There are other printable angle properties worksheets with answer keys to accompany the angles around a point worksheets with plenty of practice finding missing angles, including angles in a quadrilateral and vertically opposite angles.

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Raise maths attainment across your school with hundreds of flexible and easy to use GCSE maths worksheets and lessons designed by teachers for teachers.

Angles around a point at a glance

An angle is formed when two lines or rays intersect at a vertex. Measuring angles with a protractor on a scale diagram is one way to find the size of unknown angles., however, a more efficient method is to use known angle facts when finding missing angles or calculating angles in 2D shape problems. 

Angles around a point, or angles in a full turn, sum to 360°. So if, for example, we know that three angles ‘a’, ’b’ and ‘c’ lie around a point, and we know that angle ’a’ is a right angle, and we also know the size of angle ‘b’, we can find the size of angle ‘c’ by subtracting angle ‘b’ from 270°. 

Looking forward, students can then progress to additional angles rules worksheets and other geometry worksheets , for example an  angles in polygons worksheet  or  volume and surface area of spheres worksheet .

For more teaching and learning support on Geometry our GCSE maths lessons provide step by step support for all GCSE maths concepts.

Related worksheets

GCSE Exam Questions – Parts of a Circle

GCSE Exam Questions – Area of a Trapezium

GCSE Exam Questions – Area of Compound Shapes

GCSE Exam Questions – Bearings

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Angles around a Point (Worksheets with Answers)

Subject: Mathematics

Age range: 7-11

Resource type: Lesson (complete)

Last updated

16 January 2019

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Three differentiated worksheets ( with solutions ) that allow students to take the first steps , then strengthen and extend their skills in working with angles around a point.

Click 👉 tes.com/…/worksheets… to download similar style worksheets on other topics. These worksheets are great to use in class or as a homework. They are also excellent for one-to-one tuition and for interventions.

The download includes a special PowerPoint which allows individual questions to be enlarged and answers to questions to be revealed one at a time.

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Geometry: Angles

Related Topics: More Geometry Lessons Geometry Worksheets Geometry Games

In these lessons, we will learn the following:

How to form an Angle

• Naming an Angle
• Measuring Angles with a protractor
• Angles around a point (with worksheets)

In geometry, an angle consists of two rays that share the same endpoint. The point where the rays intersect is called the vertex of the angle. The two rays are called the sides of the angle.

Naming An Angle

You can name an angle by specifying three points: two on the rays and one at the vertex. The angle below may be specified as angle ABC or ∠ABC. The vertex point is always given in the middle.

How to name an angle? The vertex is the point where the two rays meet to form an angle. Angles can be named in three ways:

• By three capital letters, with the vertex letter in the middle. ∠ABC or ∠CBA
• By one capital letter ∠B. This can only be used if ∠B is the only angle it could be.
• By one lower case letter or number written in the middle of the angle.

Have a look at the following video for more examples on how to name angles How to name an angle using three letters

Measuring Angles

The size of an angle is measured in degrees with the use of a protractor.

A straight line has an angle of 180°

Worksheets for Angles in a straight line

How to use a protractor to measure an angle?

How to Measure a Reflex Angle Using a Protractor?

Angles Around A Point

The sum of angles around a point will always be 360 degrees.

In the diagram above, the sum of the angles is 70° + 55° + 50° + 65° + 120° = 360°

Example 1: Given the diagram below, determine the value of the angle a.

  Solution:

Step 1: Get the sum of the known angles.

30° + 65° + 150° + 73° = 318°

Step 2: Subtract sum of known angles from 360°

360° – 318° = 42°

Answer: Angle a is 42°

Worksheets for Angles Around a Point

What are angles around a point? It will also give some examples of finding angles around a point.

Problem Solving: Angles Around a Point This video discusses relationships among angles around a point.

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Angles Around a Point Worksheets

Is "angles around a point" something your students are lagging behind in? Don't worry! Our print-ready, no-prep angles around a point worksheets, some of which are free, help teachers clearly explain the concept. Practice and review this concept with this great series of printable worksheets that focus specifically on finding the unknown angle around the center of the circle, finding the missing angle around a point, and finding the value of x when the missing angle is represented as simple expression. Equipped with answer key, each worksheet pdf facilitates instant verification of answers.

Find the unknown Angle: Easy

Enhance 4th grade and 5th grade students' engagement with these printable exercises that address finding the measure of the missing angle in a circle with its center as the common endpoint of the rays. As the angles around a point always add up to 360 degrees, figuring out the missing angle requires subtracting the measure of the known angle from 360.

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Find the unknown Angle: Moderate

Help students' practice become twice as effective with this set featuring measures of two or three angles around a point. All angles around a point sum up to 360 degrees. Use this fact to find the measure of the unknown angle by adding the known angles and subtracting the sum from 360 with these pdfs.

Find the value of X

Using this bespoke resource for grade 4 and grade 5 children, you can check how well students know their angles around a point. The unknown angles are represented as simple expressions in terms of x. Form an expression by equating the sum of angles around a point to 360, and solve for x.

Related Worksheets

» Angles on a straight line

» Pairs of Angles

» Measuring Angles

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Angles Around a Point

Angles around a point will always add up to 360 degrees

 Because of this we can sometimes find an unknown angle.

Example: What is angle "c"?

To find angle c  we take the sum of the known angles and subtract that from 360°

Angles - Point, Line, Opposite, Triangle

Complete lesson on calculating angles around a point, on a line, vertically opposite and in a triangle. Tutorial and differentiated main task. Exam questions extension task. Alternative main activity (or recap resource) is an angles cross number.

Missing Angles

Related worksheets.

Find the missing angles in a triangle, around a point, in a quadrilateral, find opposite and supplementary angles, or find angles which require multi-step problem solving skills.

For more shape and space resources click here.

Game Objectives

New Maths Curriculum:

Year 3: Identify right angles, recognise that two right angles make a half-turn, three make three quarters of a turn and four a complete turn; identify whether angles are greater than or less than a right angle

Year 4: Identify acute and obtuse angles and compare and order angles up to two right angles by size

Year 5: Identify: multiples of 90°, angles at a point on a straight line and ½ a turn (total 180°); angles at a point and one whole turn (total 360°); reflex angles; and compare different angles

Year 6: Find unknown angles where they meet at a point, are on a straight line, and are vertically opposite

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Estimating Angles

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• Teachers' Resources

This game offers you an opportunity to improve your ability to estimate angles. You can either play on your own or challenge a friend. The closer you get to the target angle the more points you will score. There are four levels: Level $1: 0-90^\circ$ Level $2: 0-180^\circ$ Level $3: 0-270^\circ$ Level $4: 0-360^\circ$

You may also be interested in the other problems in our Get stuck...in Feature.

Angles on a straight line add to 180°

Example 1: Find the size of angle a

Angles on a straight line add to 180° a + 130° = 180° a = 50°

Example 2: Find the size of angle b

Angles on a straight line add to 180° b + 90° + 65° = 180° b + 155° = 180° b = 25°

Find the size of angle c:

Find the size of angle d:

Angles around a point add to 360°

Example 3: Find the size of angle e

Angles around a point add to 360° e + 295° = 360° e = 65°

Example 4: Find the size of angle f

Angles around a point add to 360° f + 131° + 108° + 52° = 360° f + 291° = 360° f = 69°

Find the size of angle g:

Angles in a triangle add to 180°

Example 5: Find the size of angle j

Angles in a triangle add to 180° j + 71° + 53° = 180° j + 124° = 180° j = 56°

Example 6: Find the size of angle k

Here we have an isosceles triangle. In an isosceles triangle two angles (and two sides) are equal. There are lines on two of the sides to show that they are equal. The other side of an isosceles triangle is called the base. The angles at the base of an isosceles triangle are equal. This means we have two 58° angles.

k + 58° + 58° = 180° k + 116° = 180° k = 64°

Example 7: Find the size of angle m

We have another isosceles triangle. This time the missing angle is at the base.

m + m + 32° = 180° 2m = 148° m = 74°

Find the size of angle n:

Find the size of angle p:

Find the size of angle q:

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Hot Oceans Worsened Dubai’s Dramatic Flooding, Scientists Say

An international team of researchers found that heavy rains had intensified in the region, though they couldn’t say for sure how much climate change was responsible.

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By Raymond Zhong

Scenes of flood-ravaged neighborhoods in one of the planet’s driest regions stunned the world this month. Heavy rains in the United Arab Emirates and Oman submerged cars, clogged highways and killed at least 21 people. Flights out of Dubai’s airport, a major global hub, were severely disrupted.

The downpours weren’t a total surprise — forecasters had anticipated the storms several days earlier and issued warnings. But they were certainly unusual.

Here’s what to know.

Heavy rain there is rare, but not unheard-of.

On average, the Arabian Peninsula receives a scant few inches of rain a year, although scientists have found that a sizable chunk of that precipitation falls in infrequent but severe bursts, not as periodic showers. These rains often come during El Niño conditions like the ones the world is experiencing now.

U.A.E. officials said the 24-hour rain total on April 16 was the country’s largest since records there began in 1949 . And parts of the nation had already experienced an earlier round of thunderstorms in March.

Oman, with its coastline on the Arabian Sea, is also vulnerable to tropical cyclones. Past storms there have brought torrential rain, powerful winds and mudslides, causing extensive damage.

Global warming is projected to intensify downpours.

Stronger storms are a key consequence of human-caused global warming. As the atmosphere gets hotter, it can hold more moisture, which can eventually make its way down to the earth as rain or snow.

But that doesn’t mean rainfall patterns are changing in precisely the same way across every part of the globe.

In their latest assessment of climate research , scientists convened by the United Nations found there wasn’t enough data to have firm conclusions about rainfall trends in the Arabian Peninsula and how climate change was affecting them. The researchers said, however, that if global warming were to be allowed to continue worsening in the coming decades, extreme downpours in the region would quite likely become more intense and more frequent.

Hot oceans are a big factor.

An international team of scientists has made a first attempt at estimating the extent to which climate change may have contributed to April’s storms. The researchers didn’t manage to pin down the connection precisely, though in their analysis, they did highlight one known driver of heavy rain in the region: above-normal ocean temperatures.

Large parts of the Indian, Pacific and Atlantic Oceans have been hotter than usual recently, in part because of El Niño and other natural weather cycles, and in part because of human-induced warming .

When looking only at El Niño years, the scientists estimated that storm events as infrequent as this month’s delivered 10 percent to 40 percent more rain to the region than they would in a world that hadn’t been warmed by human activities. They cautioned, however, that these estimates were highly uncertain.

“Rainfall, in general, is getting more extreme,” said Mansour Almazroui, a climate scientist at King Abdulaziz University in Jeddah, Saudi Arabia, and one of the researchers who contributed to the analysis.

The analysis was conducted by scientists affiliated with World Weather Attribution, a research collaboration that studies extreme weather events shortly after they occur. Their findings about this month’s rains haven’t yet been peer reviewed, but are based on standardized methods .

The role of cloud seeding isn’t clear.

The U.A.E. has for decades worked to increase rainfall and boost water supplies by seeding clouds. Essentially, this involves shooting particles into clouds to encourage the moisture to gather into larger, heavier droplets, ones that are more likely to fall as rain or snow.

Cloud seeding and other rain-enhancement methods have been tried around the world, including in Australia, China, India, Israel, South Africa and the United States. Studies have found that these operations can, at best, affect precipitation modestly — enough to turn a downpour into a bigger downpour, but probably not a drizzle into a deluge.

Still, experts said pinning down how much seeding might have contributed to this month’s storms would require detailed study.

“In general, it is quite a challenge to assess the impact of seeding,” said Luca Delle Monache, a climate scientist at the Scripps Institution of Oceanography in La Jolla, Calif. Dr. Delle Monache has been leading efforts to use artificial intelligence to improve the U.A.E.’s rain-enhancement program.

An official with the U.A.E.’s National Center of Meteorology, Omar Al Yazeedi, told news outlets that the agency didn’t conduct any seeding during the latest storms. His statements didn’t make clear, however, whether that was also true in the hours or days before.

Mr. Al Yazeedi didn’t respond to emailed questions from The New York Times, and Adel Kamal, a spokesman for the center, didn’t have further comment.

Cities in dry places just aren’t designed for floods.

Wherever it happens, flooding isn’t just a matter of how much rain comes down. It’s also about what happens to all that water once it’s on the ground — most critically, in the places people live.

Cities in arid regions often aren’t designed to drain very effectively. In these areas, paved surfaces block rain from seeping into the earth below, forcing it into drainage systems that can easily become overwhelmed.

One recent study of Sharjah , the capital of the third-largest emirate in the U.A.E., found that the city’s rapid growth over the past half-century had made it vulnerable to flooding at far lower levels of rain than before.

Omnia Al Desoukie contributed reporting.

Raymond Zhong reports on climate and environmental issues for The Times. More about Raymond Zhong