An angle of 65° is corresponding to angle a. Find a.

a = 65° (corresponding angles, parallel lines)

An angle of 112° is alternate to angle b. Find b.

b = 112° (alternate angles, parallel lines)

An angle of 74° is co-interior to angle c. Find c.

c = 106° (co-interior angles add to 180°)

Free worksheet · Australian Curriculum

Angles on parallel lines worksheets with answers

When a line crosses two parallel lines, eight angles appear, and three rules tell you all of them. Learn the rules, then practise with fresh questions and worked solutions.

Make a worksheet ↓How to do it and a quick check ↓

Topic guide

Angles on parallel lines, explained

The three angle pairs, how to spot them, and how to write the reason a test expects.

1. The transversal

A transversal is a line that crosses two or more other lines. When it crosses two parallel lines, it makes eight angles: four at each crossing. The angles at one crossing match the angles at the other, so once you know one angle you can find all eight.

2. Corresponding angles are equal (F shape)

Corresponding angles sit in the same position at each crossing, for example both above the line and to the right of the transversal. Trace an F shape to find them. If one is $65°$ , the other is $65°$ .

3. Alternate angles are equal (Z shape)

Alternate angles sit between the parallel lines, on opposite sides of the transversal. Trace a Z shape. If one is $112°$ , the other is $112°$ .

4. Co-interior angles add to 180° (C shape)

Co-interior angles sit between the parallel lines, on the same side of the transversal. Trace a C shape. They are supplementary:

$a + b = 180°$

If one is $74°$ , the other is $180° - 74° = 106°$ .

5. Two rules that work on any lines

Vertically opposite angles are equal: they are across from each other where two lines cross.
Angles on a straight line add to $180°$ .

Most questions mix these with the parallel line rules, one step at a time.

6. Using algebra, and giving reasons

If corresponding angles are $3x + 10$ and $70°$ , set them equal:

$3x + 10 = 70, 3x = 60, x = 20$

In a test, write the reason next to each step, for example "corresponding angles, parallel lines". Leaving out "parallel lines" often costs the mark, because the rule only works when the lines are parallel.

Quick check: 10 questions

Try each one, then open the answer.

An angle of $65°$ is corresponding to angle $a$ . Find $a$ .
Answer
$a = 65°$ (corresponding angles, parallel lines)
An angle of $112°$ is alternate to angle $b$ . Find $b$ .
Answer
$b = 112°$ (alternate angles, parallel lines)
An angle of $74°$ is co-interior to angle $c$ . Find $c$ .
Answer
$c = 106°$ (co-interior angles add to $180°$ )
An angle of $38°$ is vertically opposite angle $d$ . Find $d$ .
Answer
$d = 38°$
Angle $e$ and an angle of $125°$ lie on a straight line. Find $e$ .
Answer
$e = 55°$
Two co-interior angles are $x$ and $2x$ . Find $x$ .
Answer
$3x = 180$ , so $x = 60$
Two alternate angles are $4x - 10$ and $2x + 30$ . Find $x$ and the size of each angle.
Answer
$x = 20$ , and each angle is $70°$
Corresponding angles are $5x + 15$ and $80°$ . Find $x$ .
Answer
$x = 13$
Co-interior angles are $3x + 20$ and $2x + 10$ . Find $x$ .
Answer
$5x + 30 = 180$ , so $x = 30$
Angle $a$ is alternate to an angle of $47°$ , and angle $b$ is co-interior to angle $a$ . Find $a$ and $b$ .
Answer
$a = 47°$ and $b = 133°$

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These topic pages cover this skill, with worked examples, common mistakes and a question to try.

Year 7 worksheetAngles Year 7 worksheetAngles in triangles and quadrilaterals Year 8 worksheetProperties of quadrilaterals Year 10 worksheetGeometric reasoning and proofs

Questions

What are the three angle rules for parallel lines?

Corresponding angles are equal, alternate angles are equal, and co-interior angles add to 180 degrees. They only work when the two lines are parallel.

How do I remember corresponding, alternate and co-interior angles?

Use the letters: corresponding angles make an F shape, alternate angles make a Z shape, and co-interior angles make a C shape.

What year are angles on parallel lines taught?

In the Australian Curriculum, angles formed by a transversal crossing parallel lines are introduced in Year 7 and used again in later geometry.

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