Angles and Shapes
31 free practice questions with explanations
PassNova has 31 free GCSE Maths Foundation practice questions on Angles and Shapes, each with a clear explanation. Practise them in the browser with instant feedback — 100% free, no sign-up, on any device. Updated for 2026.
Angles and Shapes: example questions & answers
12 worked examples with answers and explanations below. Practise all 31 Angles and Shapes questions free in the browser, with instant feedback on every answer.
What is the sum of angles in a triangle?
- A90°
- B180°✓
- C270°
- D360°
Answer: The angles in any triangle always add up to 180°.
In a triangle, two angles are 50° and 60°. What is the third angle?
- A30°
- B60°
- C70°✓
- D120°
Answer: Third angle = 180° - 50° - 60° = 70°.
What is the sum of angles in a quadrilateral?
- A180°
- B270°
- C360°✓
- D540°
Answer: The angles in any quadrilateral add up to 360°.
What is the sum of angles in a pentagon?
- A360°
- B480°
- C540°✓
- D720°
Answer: Sum of angles = (5 - 2) × 180° = 3 × 180° = 540°.
What is the size of each interior angle in a regular hexagon?
- A90°
- B120°✓
- C135°
- D150°
Answer: Sum of angles in hexagon = (6 - 2) × 180° = 720°. Each angle = 720° ÷ 6 = 120°.
What is the size of each interior angle in a regular octagon?
- A120°
- B135°✓
- C144°
- D150°
Answer: Sum = (8 - 2) × 180° = 1080°. Each angle = 1080° ÷ 8 = 135°.
Two angles are vertically opposite. If one is 65°, what is the other?
- A25°
- B65°✓
- C115°
- D130°
Answer: Vertically opposite angles are equal. So the other angle is also 65°.
Two angles on a straight line are supplementary. If one is 35°, what is the other?
- A55°
- B65°
- C145°✓
- D155°
Answer: Angles on a straight line add up to 180°. So the other angle = 180° - 35° = 145°.
In a parallelogram, if one angle is 75°, what is the opposite angle?
- A75°✓
- B105°
- C165°
- D15°
Answer: Opposite angles in a parallelogram are equal. So the opposite angle is also 75°.
In a parallelogram, if one angle is 60°, what are the adjacent angles?
- A60° and 60°
- B60° and 120°✓
- C120° and 120°
- D60° and 90°
Answer: Adjacent angles in a parallelogram are supplementary (add to 180°). So 180° - 60° = 120°.
When two parallel lines are cut by a transversal, what can we say about alternate angles?
- AThey are supplementary
- BThey are equal✓
- CThey add to 90°
- DThey add to 270°
Answer: Alternate angles formed by parallel lines and a transversal are equal.
Two parallel lines are cut by a transversal. If one alternate angle is 55°, what is the other?
- A35°
- B55°✓
- C125°
- D145°
Answer: Alternate angles are equal, so the other angle is also 55°.