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Angle rules Angles in a triangle Angles in polygons Solving equationsThis topic is relevant for:

Here we will learn about **co-interior angles** including how to recognise co-interior angles, and apply this understanding 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.

**Co-interior angles** occur in between two parallel lines when they are intersected by a transversal. The two angles that occur on the same side of the transversal always add up to

**Co-interior angles add up to 180º **

g + h = 180^{\circ}

i + j = 180^{\circ}

k + l = 180^{\circ}

m + n = 180^{\circ}

We can often spot co-interior angles by drawing a ** C shape**.

The two interior angles are **only equal when they are both 90º**.

In all other cases we can work out one of the co-interior angles by subtracting the other from 180º.

In order to find a missing angle in parallel lines:

**Highlight the angle(s) that you already know.****State the alternate angle, co-interior angle or corresponding angle fact to find a missing angle in the diagram.****Use basic angle facts to calculate the missing angle.**

Steps

Get your free co-interior angles worksheet of 20+ questions and answers. Includes reasoning and applied questions.

COMING SOONGet your free co-interior angles worksheet of 20+ questions and answers. Includes reasoning and applied questions.

COMING SOONCalculate the size of the missing angle

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

**2Use co-interior angles to find a missing angle.**

Here we can label the co-interior angle on the diagram as

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

Here as

Calculate the size of the missing angle

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

Here we can use either the

**Use co-interior angles to find a missing angle.**

As co-interior angles have a sum of

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

Here we have a trapezium with the sum of interior angles as

\[\begin{aligned}
\theta&=360^{\circ}-\left(118^{\circ}+62^{\circ}+83^{\circ}\right) \\\\
\theta&=97^{\circ}
\end{aligned}\]

Calculate the size of the missing angle

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

We need to find the value of

** Use co-interior angles to find a missing angle.**

As

\[\begin{aligned}
11x+4x&=180^{\circ} \\
15x&=180^{\circ} \\
x&=12^{\circ}
\end{aligned}\]

This gives us the two co-interior angles of

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

The angles in the triangle are

Since \theta and 42^o are on a straight line,

\[\begin{aligned}
\theta&=180-42 \\\\
\theta&=138^{\circ}
\end{aligned}\]

**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 co-interior angles being inside the

**Using a protractor to measure an angle**

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 unless it is a coincidence.

Co-interior 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 value of \theta. Justify your answer

\theta =136^{\circ}

\theta =44^{\circ}

\theta =143^{\circ}

\theta =37^{\circ}

\theta and 44^{\circ} are co-interior angles. Therefore,

\theta = 180-44=136^{\circ}

2. Calculate the value of \theta

\theta =125^{\circ}

\theta =55^{\circ}

\theta =70^{\circ}

\theta =62.5^{\circ}

Using co-interior angles, we can calculate

180-125=55^{\circ}

Using co-interior angles again, we can see that

\theta=180-55=125^{\circ}

3. Given the information in the diagram, calculate the size of angle \theta

\theta =110^{\circ}

\theta =70^{\circ}

\theta =40^{\circ}

\theta =140^{\circ}

Using co-interior angles, we can calculate

180-110=70^{\circ}

Since it is an isosceles triangle, the other angle at the bottom of the triangle is 70^{\circ} as well.

Then, using angles in a triangle,

\theta=180-(70+70)=40^{\circ}

4. Calculate the value of \theta

\theta =90^{\circ}

\theta =95^{\circ}

\theta =85^{\circ}

\theta =83^{\circ}

(7 + \theta)^{\circ} and 88^{\circ} are co-interior angles therefore

\begin{aligned} (7+ \theta) +88&=180\\\\ \theta&=180-(88+7)\\\\ \theta&=85^{\circ} \end{aligned}

5. Work out the value of \theta

\theta =68^{\circ}

\theta =44^{\circ}

\theta =112^{\circ}

\theta =22^{\circ}

Since the triangle is an isosceles triangle, we know that the other angle at the top of the triangle is 68^{\circ}.

(\theta+68)^{\circ} and 68^{\circ} are co-interior angles therefore

(\theta+68) + 68 = 100 \theta = 180-(68+68) \theta=44\degree

6. By calculating the value for x , work out the size of each angle labelled.

42^{\circ} and 38^{\circ}

30^{\circ} and 30^{\circ}

80^{\circ} and 100^{\circ}

78^{\circ} and 102^{\circ}

3x+12 and 2x+18 are co-interior angles, and so add up to 180\degree.

Therefore, we can write

3x+12+2x+18=180

5x+30=180

5x=150

x=30

so

3x+12=3 \times 30 + 12=102\degree

2x+18=2 \times 30+18=78\degree

1.

(a) Find the size of angle x .

(b) Find the size of angle y .

**(3 marks)**

Show answer

(a)

180-38=142^{\circ} as co-inteior angles add to 180^{\circ}

180-142=38^{\circ} as angles on a straight line add to 180^{\circ}

**(2)**

(b)

180 – {(110 + 38)}=32^{\circ}

**(1)**

2. Work out the value of x .

**(3 marks)**

Show answer

5x – 7 + 3x + 11 = 180

**(1)**

8x + 4 = 180

**(1)**

x=22^{\circ}

**(1) **

3. Are the lines AB and CD parallel? Give a reason for your answer.

**(2 marks)**

Show answer

No,

95+87=182^{\circ}

**(1)**

When two lines are parallel, the co-interior angles add up to 180^{\circ}

**(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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