Year 7 - Angles in triangles and quadrilaterals - Free practice

Year 7 Angles in Triangles and Quadrilaterals Worksheets & Practice

Find missing angles using interior angle sums. Worked solutions every time, free.

Quick answer

What do the angles in a triangle and quadrilateral add up to?

The interior angles of any triangle always add up to 180°. A quadrilateral can be split into two triangles, so its angles add up to 360°. To find a missing angle, subtract the known angles from the total. For example, if two angles in a triangle are 65° and 80°, the third is 180° − 65° − 80° = 35°.

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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 in triangles and quadrilaterals: 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 · Missing angle in a triangle
A triangle has interior angles of $47°$ and $86°$ . Find the third interior angle.
Show worked solution
Key idea: The interior angles of any triangle add to $180°$ .
1. Write the angle sum equation: $47 + 86 + x = 180$
2. Add the known angles: $133 + x = 180$
3. Subtract $133$ from both sides: $x = 180 - 133 = 47$
Answer: The third angle is $47°$ .
Example 2 · Missing angle in a quadrilateral
A quadrilateral has interior angles of $115°$ , $83°$ , and $74°$ . Find the fourth interior angle.
Show worked solution
Key idea: A quadrilateral can be split into two triangles, so its interior angles sum to $2 \times 180° = 360°$ .
1. Write the angle sum equation: $115 + 83 + 74 + x = 360$
2. Add the known angles: $272 + x = 360$
3. Subtract $272$ from both sides: $x = 360 - 272 = 88$
Answer: The fourth angle is $88°$ .
Example 3 · Unknown angle in a real-life triangular frame
A builder is making a triangular roof frame. One angle at the base of the triangle is $54°$ and the other base angle is $38°$ . The timber at the top of the frame must be cut so that the pieces meet at exactly the right angle. What is the angle at the top of the frame?
Show worked solution
Key idea: The three interior angles of any triangle sum to $180°$ .
1. Let the angle at the top be $x$ .
2. Write the angle sum equation: $54 + 38 + x = 180$
3. Add the known angles: $92 + x = 180$
4. Subtract $92$ from both sides: $x = 180 - 92 = 88$
Answer: The angle at the top of the frame is $88°$ .

Common mistakes

Where students usually lose marks

Using 360° for a triangle

Wrong: $47 + 86 + x = 360$ , so $x = 227°$

The angle sum of $360°$ applies to quadrilaterals, not triangles. Always use $180°$ for a triangle.

Using 180° for a quadrilateral

Wrong: $115 + 83 + 74 + x = 180$ , giving a negative answer

A quadrilateral's angles sum to $360°$ , not $180°$ . Remember: split it into two triangles and double the triangle sum.

Adding instead of subtracting to find the unknown

Wrong: $47 + 86 = 133$ , so $x = 180 + 133 = 313°$

Once you have the sum of the known angles, subtract it from the total angle sum to find the missing angle.

Forgetting that all angles in a rectangle are 90°

Wrong: treating a rectangle as if only two angles are $90°$ and solving for two unknowns

A rectangle has four right angles, each equal to $90°$ . Use this fact first before writing any equation.

Try one yourself

Your turn

A triangle has two angles of $47°$ and $82°$ . What is the size of the third angle in degrees?

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About this worksheet

Why we built it

In Year 7, students learn why the angles inside any triangle always add to 180°, then use that fact to work out the angle sum of quadrilaterals and other polygons. These worksheets build from identifying angle types all the way to finding unknown angles in multi-step problems, with full worked solutions so students can follow each line of reasoning.

What's covered

Sub-skills your student will practise

✓Demonstrating that the interior angles of a triangle sum to 180°
✓Finding a missing angle in a triangle given the other two
✓Using the triangle angle sum to derive the angle sum of a quadrilateral (360°)
✓Finding missing angles in quadrilaterals including rectangles and parallelograms
✓Extending the angle sum rule to pentagons, hexagons and other polygons
✓Solving simple equations to find unknown angles in triangles and quadrilaterals

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Frequently asked

Questions parents ask about angles in triangles and quadrilaterals

Why do the angles in a triangle always add up to 180°?

If you tear off the three corners of any triangle and place them side by side, they always form a straight line, which is 180°. This works for every triangle, no matter its shape or size.

How do you find the angle sum of a quadrilateral from the triangle rule?

Any quadrilateral can be split into two triangles by drawing one diagonal. Each triangle has an angle sum of 180°, so the quadrilateral has an angle sum of 2 × 180° = 360°.

Does the interior angle sum rule work for all polygons, not just triangles and quadrilaterals?

Yes. A polygon with n sides can be split into (n - 2) triangles, giving an interior angle sum of (n - 2) × 180°. For a pentagon that is 3 × 180° = 540°, for a hexagon it is 4 × 180° = 720°.

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