Geometry Angles and Symmetry (Class 5)

What this worksheet covers

This is an eighteen-question practice worksheet on geometry — angles, shapes and symmetry for Class 5, written to the pattern of the SOF International Mathematics Olympiad (IMO). It carries 24 marks and is designed to be attempted in 45 minutes, split across three sections — Mathematical Reasoning, Everyday Mathematics and Reasoning and Achievers Section. Every question is multiple choice with exactly one correct option, and every one comes with a fully worked solution rather than just an answer key — so a child who gets one wrong can see where the reasoning went astray instead of only learning that it did.

Skills your child practises

• Applied problem-solving on geometry — angles, shapes and symmetry at Class 5 level
• Working accurately against a time limit, as the real paper demands
• Mathematical Reasoning questions in the olympiad format
• Everyday Mathematics and Reasoning questions in the olympiad format
• Achievers Section questions in the olympiad format
• Reading worked solutions to find the step that went wrong

How to use it

1. 1There are 18 questions in this worksheet. All questions are compulsory.
2. 2Each question has four options (A), (B), (C) and (D). Exactly one option is correct.
3. 3Questions 1–15 carry 1 mark each. Questions 16–18 (Achievers Section) carry 3 marks each.
4. 4There is no negative marking. Use of a calculator is not allowed.
5. 5Figures are not drawn to scale.

Sample questions from this worksheet

A preview of what's inside Geometry Angles and Symmetry (Class 5) — the PDF has the full set, and every question comes with a worked solution like these.

1. 1. An angle that measures less than 90° is called a/an _______ angle.

   • AAcutecorrect
   • BRight
   • CObtuse
   • DReflex
   Solution: An acute angle is less than 90°. A right angle is exactly 90°, an obtuse angle is between 90° and 180°, and a reflex angle is more than 180°.

2. 2. Two angles of a triangle measure 65° and 45°. The third angle is _______.

   • A70°correct
   • B60°
   • C80°
   • D110°
   Solution: The three angles add up to 180°.
   Third angle = 180° − (65° + 45°) = 180° − 110° = 70°.

3. 3. Consider the following statements.(i) A circle has infinitely many lines of symmetry.(ii) A triangle can have two right angles.(iii) The diameter is the longest chord of a circle.Which of the statements is/are correct?

   • A(i) and (ii) only
   • B(i) and (iii) onlycorrect
   • C(ii) and (iii) only
   • DAll three
   Solution: Statement (i) is true — any line through the centre folds a circle onto itself. Statement (ii) is false; two right angles already use up 180°, leaving nothing for the third angle. Statement (iii) is true; every chord is shorter than the one that passes through the centre. Hence (i) and (iii).