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Angle rules Angles in a trianglesAngles in a quadrilateral

Forming and solving equationsThis topic is relevant for:

Here we will learn about **corresponding angles **including how to recognise when angles are corresponding and apply this to solve problems.

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

**Corresponding angles** are angles that occur on the same side of the transversal line and are **equal **in size. They are either both obtuse or both acute.

**Corresponding angles are equal **

We can often spot corresponding angles by drawing an F shape.

In order to calculate with corresponding angles:

**Highlight the angle(s) that you already know.****Use corresponding angles to find a missing angle.****Use a basic angle fact to calculate the missing angle**.

Get your free Corresponding angles worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREEGet your free Corresponding angles worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREECalculate the size of the missing angle

**Highlight the angle(s) that you already know.**

2** ****Use corresponding angles to find a missing angle.**

Here we can label the corresponding angle on the diagram as

3**Use a basic angle fact to calculate the missing angle.**

Here ^{°}

\[\begin{aligned}
\theta&=180^{\circ}-75^{\circ} \\
\theta&=105^{\circ}
\end{aligned}\]

Calculate the size of the missing angle

**Highlight the angle(s) that you already know.**

** Use corresponding angles to find a missing angle. **

We can identify two new angles of ^{°}^{°}

**Use a basic angle fact to calculate the missing angle.**

As the sum of angles in a triangle is ^{°}

\[\begin{aligned}
\theta&=180^{\circ}-\left(63^{\circ}+56^{\circ}\right) \\
\theta&=61^{\circ}
\end{aligned}\]

Calculate the size of the missing angle

**Highlight the angle(s) that you already know.**

Here we need to find the value for

** Use corresponding angles to find a missing angle. **

The relative position of the two angles

\[\begin{aligned}
4x-14&=3 x+7 \\
4x&=3x+21 \\
x&=21^{\circ}
\end{aligned}\]

As ^{°}^{°}

**Use a basic angle fact to calculate the missing angle.**

Here we can combine the fact that we have an isosceles triangle and the sum of angles on a straight line is ^{°}

As the triangle is isosceles with the base of the triangle on one parallel line, the angles either side of the top vertex of the triangle are symmetrical (this can also be calculated using the alternate angle rule).

These angles form a straight line, and as angles on a straight line add to 180 we can therefore find

\[\begin{aligned}
\theta&=180-(70+70) \\
\theta&=40^{\circ}
\end{aligned}\]

**Mixing up angle facts**

There are a lot of angle facts and it is easy to mistake alternate angles with corresponding angles. To prevent this from occurring, think about corresponding angles as being underneath the F shape.

**Using a protractor to measure an angle**

Most diagrams are not to scale and so using a protractor will not result in a correct answer.

Corresponding angles is part of our series of lessons to support revision on angles in parallel lines. You may find it helpful to start with the main angles in parallel lines 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. Calculate the size of angle \theta

\theta=96^{\circ}

\theta=84^{\circ}

\theta=264^{\circ}

\theta=74^{\circ}

Using corresponding angles, we can see the angle 96^{\circ} . We can then use angles on a straight line: \theta=180-96=84^{\circ} .

2. Calculate the value of \theta .

\theta=72^{\circ}

\theta=36^{\circ}

\theta=108^{\circ}

\theta=144^{\circ}

Using corresponding angles, we can see the angle \theta=72^{\circ} . We can then use angles on a straight line: \theta=180-72=108^{\circ}

3. Work out the size of angle \theta

\theta=60^{\circ}

\theta=58^{\circ}

\theta=62^{\circ}

\theta=122^{\circ}

We start by calculating the missing angle in the triangle: 180-(62+60)=58 . We can then use corresponding angles to see that \theta=58^{\circ} .

4. Calculate the value for angle \theta

\theta=106^{\circ}

\theta=95^{\circ}

\theta=115^{\circ}

\theta=65^{\circ}

Using corresponding angles, we can see that \theta is corresponding to 106+11 therefore \theta=106+11=115^{\circ}

5. Calculate the size of angle \theta

\theta=12^{\circ}

\theta=97^{\circ}

\theta=109^{\circ}

\theta=85^{\circ}

Using corresponding angles, we can see the angle 97^{\circ} . Since vertically opposite angles are equal, the angle opposite is also 97^{\circ} . Using corresponding angles we can also see the angle 12^{\circ} . Then \theta=97-12=85^{\circ} .

6. By calculating the value for x , work out the size of each of the corresponding angles labelled in the diagram.

45^{\circ} \text{ and } 45^{\circ}

45^{\circ} \text{ and } 135^{\circ}

30^{\circ} \text{ and } 20^{\circ}

50^{\circ} \text{ and } 50^{\circ}

3x and 5x-30 are corresponding angles and so are equal. Therefore we can write 3x=5x-30 .

We can then solve this:

\begin{aligned}
3x&=5x-30\\
0&=2x-30\\
30&=2x\\
15&=x
\end{aligned}

\begin{array}{l}
3\times 15 = 45^{\circ}\\
5\times 15-30 = 45^{\circ}
\end{array}

1.

(a) Work out the size of angle m. Give reasons for your answer.

(b) Work out the size of angle n.

**(4 marks)**

Show answer

(a) m and 74 ^{\circ} are corresponding

**(1)**

m=74^{\circ}

**(1)**

(b) Corresponding angles are equal:

**(1)**

Angles on a straight line add to 180 so,

180-74=106^{\circ}

**(1)**

2.

(a) Work out the size of angle a.

(b) Work out the size of angle b.

**(3 marks)**

Show answer

(a) a=37^{\circ} as corresponding angles are equal

**(1)**

(b) 98^{\circ} is corresponding with b+37^{\circ}

so b+37=98

**(1)**

b=61^{\circ}

**(1)**

3. Work out the value of x .

**(3 marks)**

Show answer

Opposite angles equal

**(1)**

2x+9=4x-3 as corresponding angles are equal

**(1)**

\begin{aligned} 2x+9&=4x-3\\ 9&=2x-3\\ 12&=2x\\ 6&=x \end{aligned}

**(1)**

You have now learned how to:

- Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles
- Understand and use the relationship between parallel lines and alternate and corresponding angles

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

Download free

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.