Understand the rule first
Name the geometric relationship before calculating: a straight line totals 180°, around a point totals 360°, and a triangle totals 180°.
Angles, shapes & geometry 11+ practice
Use angle totals and shape properties to calculate missing information.
A triangle has angles 48° and 67°. Find the third angle.
- Angles in a triangle total 180°.
- 48° + 67° = 115°.
- 180° − 115° = 65°.
A common misconception
Choosing an operation from the picture without first identifying the relevant angle rule.
Reusable method: Mark every known equal side, angle or line relationship.Question 1 of 10 MathscoreAn angle on a straight line is beside an angle of 132°. What is the missing angle?
- A38°
- B58°
- C228°
- D48°
Need a hint?
The two adjacent angles total 180°.
Show worked answer
Answer D: 48°
180° − 132° = 48°.
Quick method: Mark every known equal side, angle or line relationship.
Question 2 of 10 MathscoreAn isosceles triangle has a top angle of 40°. What is each equal base angle?
- A40°
- B60°
- C140°
- D70°
Need a hint?
Remove the top angle, then share the remainder equally.
Show worked answer
Answer D: 70°
180° − 40° = 140°; 140° ÷ 2 = 70°.
Quick method: Mark every known equal side, angle or line relationship.
Question 3 of 10 MathscoreA regular octagon has how many lines of symmetry?
- A4
- B6
- C10
- D8
Need a hint?
For a regular polygon, relate symmetry lines to the number of sides.
Show worked answer
Answer D: 8
A regular octagon has eight sides and eight lines of symmetry.
Quick method: Mark every known equal side, angle or line relationship.
Question 4 of 10 Mathsexam-styleThe angles in a quadrilateral are 82°, 91°, 107° and x. Find x.
- A70°
- B90°
- C100°
- D80°
Need a hint?
Angles in a quadrilateral total 360°.
Show worked answer
Answer D: 80°
82 + 91 + 107 = 280; 360 − 280 = 80°.
Quick method: Mark every known equal side, angle or line relationship.
Question 5 of 10 Mathsexam-styleTwo equal angles and one 36° angle form a straight line. What is each equal angle?
- A62°
- B82°
- C144°
- D72°
Need a hint?
Subtract 36° from 180°, then divide the remainder by two.
Show worked answer
Answer D: 72°
180° − 36° = 144°; 144° ÷ 2 = 72°.
Quick method: Mark every known equal side, angle or line relationship.
Question 6 of 10 MathscoreTwo angles in a triangle are 48° and 67°. What is the third angle?
- A55°
- B62°
- C65°
- D75°
Need a hint?
Angles in a triangle total 180°.
Show worked answer
Answer C: 65°
48° + 67° = 115°, so the third angle is 180° − 115° = 65°.
Quick method: Mark every known equal side, angle or line relationship.
Question 7 of 10 MathscoreWhat is each exterior angle of a regular octagon?
- A22.5°
- B40°
- C60°
- D45°
Need a hint?
Exterior angles of any polygon total 360°.
Show worked answer
Answer D: 45°
A regular octagon has eight equal exterior angles: 360° ÷ 8 = 45°.
Quick method: Mark every known equal side, angle or line relationship.
Question 8 of 10 MathscoreTwo straight lines cross. One angle is 112°. What is the size of an adjacent angle?
- A68°
- B78°
- C112°
- D248°
Need a hint?
Adjacent angles on a straight line total 180°.
Show worked answer
Answer A: 68°
180° − 112° = 68°.
Quick method: Mark every known equal side, angle or line relationship.
Question 9 of 10 MathsexamAn isosceles triangle has an apex angle of 38°. What is the size of each equal base angle?
- A52°
- B71°
- C76°
- D142°
Need a hint?
Subtract the apex angle from 180°, then share the remainder equally.
Show worked answer
Answer B: 71°
The base angles total 180° − 38° = 142°. Each is 142° ÷ 2 = 71°.
Quick method: Mark every known equal side, angle or line relationship.
Question 10 of 10 MathsstretchThe interior angles of a polygon total 900°. How many sides does it have?
- A5
- B6
- C7
- D8
Need a hint?
Use (number of sides − 2) × 180°.
Show worked answer
Answer C: 7
900° ÷ 180° = 5, so n − 2 = 5 and n = 7 sides.
Quick method: Mark every known equal side, angle or line relationship.