Year 7 - Angles - Free practice

Year 7 Angles Worksheets & Practice Tests

Parallel lines, transversals, angle sums - all in one place.

Quick answer

What are corresponding, alternate and co-interior angles on parallel lines?

When a transversal crosses parallel lines, corresponding angles are equal (F-shape), alternate angles are equal (Z-shape), and co-interior angles add to 180° (C-shape). For example, if one co-interior angle is 110°, the other is 70°, because 110° + 70° = 180°.

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Six questions across Foundation, Standard and Extension, with full worked solutions, written to the Australian Curriculum.

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Worked examples

Year 7 angles: worked examples

Three examples, from a standard question to a worded problem. Have a go at each one before you open the solution.

Example 1 · Complementary and supplementary angles
Angle $a$ and angle $b$ are supplementary. Angle $a = 113°$ . Find angle $b$ .
Show worked solution
Key idea: Supplementary angles add to $180°$ .
1. Write the relationship: $a + b = 180°$
2. Substitute the known angle: $113° + b = 180°$
3. Solve for $b$ : $b = 180° - 113° = 67°$
Answer: $b = 67°$
Example 2 · Angles formed by a transversal and parallel lines
Two parallel lines are crossed by a transversal. One co-interior angle is $74°$ . Find the other co-interior angle, giving a reason.
Show worked solution
Key idea: Co-interior angles (also called C-angles) are between the parallel lines on the same side of the transversal, and they add to $180°$ .
1. Write the co-interior angle relationship: $74° + x = 180°$
2. Solve for $x$ : $x = 180° - 74° = 106°$
3. State the reason: co-interior angles on parallel lines are supplementary.
Answer: The other co-interior angle is $106°$ .
Example 3 · Finding an unknown angle in a real-life triangle
A builder cuts a triangular wooden brace. One corner of the triangle is a right angle ( $90°$ ) and another corner measures $37°$ . What is the size of the third angle of the brace?
Show worked solution
Key idea: The interior angles of a triangle add to $180°$ .
1. Write the angle sum: $90° + 37° + x = 180°$
2. Add the known angles: $127° + x = 180°$
3. Solve for $x$ : $x = 180° - 127° = 53°$
4. Check: $90° + 37° + 53° = 180°$ ✓
Answer: The third angle is $53°$ .

Common mistakes

Where students usually lose marks

Mixing up co-interior and alternate angles

Two alternate angles add to $180°$ , so $x = 180° - 65° = 115°$ .

Alternate angles (Z-angles) on parallel lines are equal, not supplementary. It is co-interior angles (C-angles) that add to $180°$ . Always check which shape the angle pair forms: Z for alternate, C for co-interior.

Confusing complementary and supplementary

Angles are supplementary, so $35° + x = 90°$ .

Complementary angles add to $90°$ , and supplementary angles add to $180°$ . A helpful memory trick: C comes before S in the alphabet, and $90$ comes before $180$ , so Complementary goes with $90°$ and Supplementary goes with $180°$ .

Assuming corresponding angles without checking the lines are parallel

These must be corresponding angles, so they are equal.

Corresponding angles are equal only when the two lines cut by the transversal are parallel. If the question does not state the lines are parallel, you cannot use this rule.

Forgetting that the angle sum applies to the interior angles of a triangle

A triangle has three angles, so each angle is $180° \div 3 = 60°$ .

The interior angles of any triangle add to $180°$ , but that does not mean they are all equal. Only an equilateral triangle has three $60°$ angles. Always use the known angles to find the unknown one.

Try one yourself

Your turn

Two parallel lines are cut by a transversal. One co-interior angle is $63°$ . Find the other co-interior angle, in degrees.

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About this worksheet

Why we built it

Angle work in Year 7 is mostly about naming the right relationship (corresponding, alternate, co-interior, vertically opposite) and using it to solve for an unknown. These worksheets drill that exact reasoning - the part students lose marks on most often in tests.

What's covered

Sub-skills your student will practise

✓Complementary, supplementary and vertically opposite angles
✓Corresponding angles on parallel lines
✓Alternate angles (Z and reverse-Z)
✓Co-interior (C) angles
✓Interior angle sum of triangles and other polygons

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Parents on the practice questions.

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Frequently asked

Questions parents ask about angles

What angle relationships does Year 7 cover?

Year 7 introduces corresponding, alternate, co-interior, and vertically opposite angles - all the relationships that arise when parallel lines are crossed by a transversal. Plus complementary (add to 90) and supplementary (add to 180) angles.

What's the easiest way to spot alternate angles?

Alternate angles form a Z-shape (or backwards Z) across two parallel lines and a transversal. Co-interior angles form a C-shape (or backwards C). Drawing the letter on top of the figure helps students identify which pair the question is asking about.

Why is the triangle angle sum 180 degrees?

It's a consequence of parallel-line angle relationships - if you draw a line parallel to one side of a triangle through the opposite vertex, the angles at that vertex form a straight line, which sums to 180. This proof is part of Year 7.

Are there other polygons whose angle sums students need to know?

Quadrilateral (360), pentagon (540), hexagon (720) - all derived from the triangle sum by splitting the polygon into triangles. The general rule (n - 2) x 180 isn't formally required at Year 7 but many teachers introduce it.

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