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Types of angles Collecting like terms Solving equationsThis topic is relevant for:

Here we will learn about **angles on a straight line**, including the sum of angles on a straight line, how to find missing angles, and using these angle facts to generate equations and solve problems.

There are also angles on a straight line worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

**Angles on a straight line** relate to the sum of angles that can be arranged together so that they form a straight line.

**Angles on a straight line add to 180°**.

Let us look at this visually:

Let’s take the three angles of

**right angle** as it measures

If we move these three angles so that each vertex meets, we get an arrangement that looks like this:

These three angles create a straight line.

By adding together

We can also look at this in reverse by considering how many degrees it takes to do a full turn.

If you stand facing North, and turn to face East, you have turned

We can therefore state that the sum of angles on a straight line is equal to ** 180°**. If we split any straight line into smaller angles, all of these angles would add to make

**Step by step guide:** Angles in a triangle

Angles in a straight line are a problem solving tool for many geometric problems. These include: properties of shapes, circle theorems, angles in parallel lines, calculating angles in shapes (interior and exterior angles), trigonometry and more.

In order to find missing angles in a quadrilateral:

**Add all known****angles.****Subtract the angle sum from**180° .**Form and solve the equation.**

Get your free angles on a straight line worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREEGet your free angles on a straight line worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREE**Add all known angles.**

\[78^{\circ}\]

**2Subtract the angle sum from 180°.**

\[180-78=102^{\circ}\]

\[x=102^{\circ}\]

**Add all known angles.**

\[154^{\circ}\]

**Subtract the angle sum from **

\[180-154=26^{\circ}\]

\[x=26^{\circ}\]

**Add all known angles.**

\[90+47= 137\]

**Subtract the angle sum from 180°. **

\[180-137=43^{\circ}\]

\[x=43^{\circ}\]

**Add all known angles.**

As

\[112\]

**Subtract the angle sum from 180°. **

\[180-112=68^{\circ}\]

\[BOD=68^{\circ}\]

\[AOD = 180 – BOD = 180-68 = 112^{\circ}\]

\[AOD=112^{\circ}\]

**Form and solve the equation.**

As

This example shows that **vertically opposite angles are equal**.

**Add all known angles.**

\[60+3x+x+10+2x+20=6x+90\]

**Form and solve the equation.**

Angles on a straight line add up to

As

\[3x=3\times15=45^{\circ}\]

\[x+10=15+10=25^{\circ}\]

\[2x+20=2\times15+20=50^{\circ}\]

We can check the solution by adding up the angles:

\[60+45+25+50=180^{\circ}\]

**Add all known angles.**

\[90+45=135\]

**Form and solve the equation.**

\[180-135=6x\]

°**The sum of angles on a straight line is equal to 360**

The angle sum is remembered incorrectly as

**Solving equations**

There are many misconceptions around forming and solving equations. See the lesson on Solving Equations for further information.**Step by step guide:** Solving equations

**Using a protractor**

When you are asked to calculate a missing angle, a common error is to use a protractor to measure the angle. When using angle facts to determine angles, diagrams are deliberately not drawn to scale unless the angle is

Angles on a straight line is part of our series of lessons to support revision on angle rules. You may find it helpful to start with the main angle rules lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

1. AOB is a straight line. Calculate the size of angle x .

95^{\circ}

25^{\circ}

115^{\circ}

295^{\circ}

180-65=115^{\circ}

2. AOB is a straight line. Calculate the size of angle x .

238^{\circ}

58^{\circ}

32^{\circ}

122^{\circ}

180-122=58^{\circ}

3. Calculate the size of the angle 2x . Hence find the value of x .

26^{\circ}

52^{\circ}

76^{\circ}

116^{\circ}

2x+90+38=180

2x+128=180

4. AB and CD are straight lines. Calculate the size of angle BOD. Hence find the value of x .

8^{\circ}

40^{\circ}

220^{\circ}

12^{\circ}

5x+140=180

5. AOB is a straight line. By finding the value for x , calculate the size of each angle in the diagram below.

x=35^{\circ}, COD=175^{\circ}, DOE=15^{\circ}, EOB=165^{\circ}

x=12.5^{\circ}, COD=72.5^{\circ}, DOE=7.5^{\circ}, EOB=75^{\circ}

x=11.1^{\circ}, COD=55.5^{\circ}, DOE=8.9^{\circ}, EOB=69.4^{\circ}

x=2.05^{\circ}, COD=10.2^{\circ}, DOE=17.95^{\circ}, EOB=33.18^{\circ}

The circle with centre C has a tangent at point O. Calculate the value of x correct to 2 decimal places.

19.11^{\circ}

10.59^{\circ}

9.11^{\circ}

5.29^{\circ}

1. Given that the sum of exterior angles of any regular polygon is equal to 360^{\circ} , calculate the interior angle of a regular pentagon.

**(2 marks)**

Show answer

360\div5=72^{\circ}

**(1)**

180-72=108^{\circ}

**(1)**

2.

(a) 3 straight lines intersect to form a triangle.

Calculate the size of angle x .

(b) What type of triangle is ABC?

**(4 marks)**

Show answer

a)

180-131=49

**(1)**

180-87=93

**(1)**

x=180-(93+49)=38^{\circ}

**(1)**

b)

A scalene triangle.

**(1)**

3. AB and CD are parallel lines. OE transects both lines.

Calculate the value of x .

**(3 marks)**

Show answer

4x+22.4=180

**(1)**

4x=157.6

**(1)**

x=39.4^{\circ}

**(1)**

4. AB is a straight line that is a tangent to the circle at point O. Show that OCD is a right angle triangle.

**(3 marks)**

Show answer

ODC=180-112=68^{\circ}

**(1)**

180-(68+22)=90^{\circ}

**(1)**

One angle in triangle OCD is equal to 90^{\circ} so it is a right angle triangle.

**(1)**

You have now learned how to:

- Find unknown angles on a straight line

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#### FREE GCSE Maths Practice Papers - 2022 Topics

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Practice paper packs based on the advanced information for the Summer 2022 exam series from Edexcel, AQA and OCR.

Designed to help your GCSE students revise some of the topics that will come up in the Summer exams.