The idea, step by step
A straight angle is a half-turn
A straight line through a vertex makes a half-turn, or 180°. When adjacent angles fill that half-turn without gaps or overlaps, their sizes add to 180°. Adjacent angles share a vertex and one arm.
To find one missing angle, subtract the known angle from 180°. The size of the missing angle is not determined by the length of its drawn arms.
More than two parts
A straight angle can be split into three or more adjacent parts. Add all the known parts first, then subtract their total from 180°. Include only the angles filling that same straight angle.
Check by adding your answer to the given angles. Their total must be exactly 180°. Write the degree symbol, and explain that the angles lie on a straight line.
A common trap
Adding the known angle to 180° to find its neighbour.
Instead: The two parts together already equal 180°, so subtract the known part.
See the thinking
Two adjacent angles
A 65° angle and x fill the straight angle shown. Find x.
- Angles on a straight line total 180°.
- x = 180° − 65° = 115°.
Three adjacent parts
A straight angle is split into 90°, 35° and x. Find x.
- Known total: 90° + 35° = 125°.
- Missing angle: 180° − 125° = 55°.
- Check: 90° + 35° + 55° = 180°.
Check your understanding
Two adjacent angles form a straight angle. One is 48°. Find the other.
Show answer
132°
180° − 48° = 132°.
Your turn
6 questions · 9 marks · Work at your own pace.
Read the questions online
- Two adjacent angles form a straight angle. One is 72°. Find the other.1 mark
- One of two adjacent angles on a straight line is 137°. Find its neighbour.1 mark
- A straight angle is split into 40°, 65° and x. Find x.2 marks
- Two equal angles fill a straight angle. Find each angle.1 mark
- Can two adjacent angles of 95° and 85° fill a straight angle? Explain.2 marks
- Noah says the angle next to a 48° angle on a straight line is 228°, because 180 + 48 = 228. Correct his method and answer.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Two adjacent angles form a straight angle. One is 72°. Find the other.1 mark
180° − 72° = 108°.
108° - One of two adjacent angles on a straight line is 137°. Find its neighbour.1 mark
180° − 137° = 43°.
43° - A straight angle is split into 40°, 65° and x. Find x.2 marks
40° + 65° = 105°.
180° − 105° = 75°.
75° - Two equal angles fill a straight angle. Find each angle.1 mark
180° shared equally between two angles gives 90° each.
90° - Can two adjacent angles of 95° and 85° fill a straight angle? Explain.2 marks
95° + 85° = 180°, so they can fill the half-turn.
Yes. - Noah says the angle next to a 48° angle on a straight line is 228°, because 180 + 48 = 228. Correct his method and answer.2 marks
The parts together total 180°.
180° − 48° = 132°.
48° + 132° = 180°.
Subtract instead: the missing angle is 132°.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics
Year 6 angle relationships: straight-line angles, angles around a point, vertically opposite angles and connected reasoning.
Official curriculum source ↗