The idea, step by step
Choose the whole or the pair
Start by describing the diagram in words. Are the required parts on a straight line, around a point, or vertically opposite? Choose 180°, 360° or equality for that reason.
Label an unknown angle with a letter. You do not need complicated algebra: state the total, add known parts and subtract. A rough-looking drawing should not overrule its stated angle values.
Show a chain of reasons
In a linked problem, calculate one useful angle at a time and write why the step works. The first result may give a missing part of a straight angle or identify an opposite angle.
Check the final values against all the givens. If an angle you found is negative, or the parts exceed the whole turn, reread the diagram instead of accepting the result. Give degrees and a sentence explaining the rule used.
A common trap
Writing an answer from how large the angle looks without stating a rule.
Instead: Use the labelled values and an angle fact. The picture helps identify the relationship; the fact justifies the calculation.
See the thinking
Two known parts
A straight angle contains adjacent parts 42°, 65° and x. Find x and explain.
- The three parts lie on a straight line, so their total is 180°.
- 42° + 65° = 107°.
- x = 180° − 107° = 73°.
Use an opposite angle, then a neighbour
At a crossing, a given angle is 116°. Angle a is vertically opposite it. Angle b is adjacent to a. Find a and b.
- a = 116° because opposite angles are equal.
- a and b form a straight angle.
- b = 180° − 116° = 64°.
Check your understanding
A straight angle has parts 25°, 80° and x. Find x and name the rule.
Show answer
75°; adjacent angles on a straight line total 180°.
180° − (25° + 80°) = 75°.
Your turn
6 questions · 12 marks · Work at your own pace.
Read the questions online
- A straight angle is divided into 45°, 68° and x. Find x.2 marks
- Four angles around a point are 50°, 75°, 95° and x. Find x.2 marks
- Two lines cross. One angle is 132°. Find its opposite angle and an adjacent angle.2 marks
- A right angle is divided into 29° and x. Find x.1 mark
- A student says 115° and 75° are adjacent angles on a straight line. Explain the error and correct the second angle.2 marks
- A full turn contains one angle of 80° and two equal angles. Find the equal angles and check your result.3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- A straight angle is divided into 45°, 68° and x. Find x.2 marks
45 + 68 = 113.
180 − 113 = 67.
67° - Four angles around a point are 50°, 75°, 95° and x. Find x.2 marks
50 + 75 + 95 = 220.
360 − 220 = 140.
140° - Two lines cross. One angle is 132°. Find its opposite angle and an adjacent angle.2 marks
Opposite angles are equal.
180° − 132° = 48°.
Opposite 132°; adjacent 48°. - A right angle is divided into 29° and x. Find x.1 mark
A right angle is 90°.
90° − 29° = 61°.
61° - A student says 115° and 75° are adjacent angles on a straight line. Explain the error and correct the second angle.2 marks
115° + 75° = 190°, not 180°.
180° − 115° = 65°.
Their total is 190°; the second angle should be 65°. - A full turn contains one angle of 80° and two equal angles. Find the equal angles and check your result.3 marks
360° − 80° = 280°.
280° ÷ 2 = 140°.
80° + 140° + 140° = 360°.
140° each
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 ↗