The idea, step by step
Choose the relationship
A straight angle is 180°, a full turn is 360°, and triangle interior angles total 180°. Mark given facts before calculating. A drawing can suggest, but cannot prove, parallel lines or equal sides.
For parallel lines, corresponding and alternate angles are equal. Co-interior angles total 180°. Name the fact that applies rather than calling every angle pair corresponding.
Build a chain of reasons
Find an intermediate angle when necessary, then use it in a triangle or straight-line sum. Check the final result against all the given information.
An n-sided polygon has interior sum (n−2)×180°, found by dividing it into triangles. Divide this sum by n only if the polygon is regular; unequal polygon angles cannot be averaged to find an individual angle.
A common trap
Angles that look equal must be equal.
Instead: Use stated facts or a theorem. The sketch may not be to scale.
See the thinking
Triangle sum
A triangle has angles 48° and 67°. Find the third angle.
- The interior sum is 180°.
- 48°+67°=115°.
- 180°−115°=65°.
Adjacent angles
Find the acute angle x next to 122° at the upper intersection.
- These adjacent angles form a straight line.
- x+122°=180°.
- x=58°. Matching angles at the lower parallel line can also be found from this.
Check your understanding
A triangle has angles 35° and 82°. Find the third.
Show answer
63°
Their sum is 117°; subtract it from 180°.
Your turn
6 questions · 13 marks · Work at your own pace.
Read the questions online
- Two adjacent angles form a straight line. One is 136°. Find the other.2 marks
- Angles around a point are 85°, 140° and x. Find x.2 marks
- A triangle has angles 72° and 49°. Find its third angle.2 marks
- Two parallel lines are crossed by a transversal. An angle at the first crossing is 71°. Find its corresponding angle at the second crossing.2 marks
- A quadrilateral has angles 88°, 97°, 104° and x. Find x.2 marks
- Find one interior angle of a regular hexagon. Explain why division by 6 is valid.3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Two adjacent angles form a straight line. One is 136°. Find the other.2 marks
Adjacent angles on a line total 180°.
180°−136°=44°.
44° - Angles around a point are 85°, 140° and x. Find x.2 marks
Angles around a point total 360°.
360°−85°−140°=135°.
135° - A triangle has angles 72° and 49°. Find its third angle.2 marks
Triangle sum is 180°.
180°−72°−49°=59°.
59° - Two parallel lines are crossed by a transversal. An angle at the first crossing is 71°. Find its corresponding angle at the second crossing.2 marks
Corresponding angles in parallel lines are equal.
71° - A quadrilateral has angles 88°, 97°, 104° and x. Find x.2 marks
Its interior angles total 360°.
360°−88°−97°−104°=71°.
71° - Find one interior angle of a regular hexagon. Explain why division by 6 is valid.3 marks
The angle sum is (6−2)×180°=720°.
Regular means all six angles are equal.
720°÷6=120°.
120°
Curriculum reference & lesson scope
Australian Curriculum v9 / South Australian Curriculum
Angle reasoning consolidation; enlargements using coordinates/digital geometry; invariant and changing properties; geometric constructions; sequences of steps and decisions; testing/refining construction algorithms; explaining geometric reasoning.
Official curriculum source ↗