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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.

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

COMING SOON**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

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

- Interior angles of a polygon
- Exterior angles of a polygon
- Angles around a point
- Angles in a quadrilateral
- Circle theorems

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