Opposite Angles: Problem Solving & Reasoning
Mathematics
GCSE Higher
14 questions
~28 mins
1 views0 downloads
About This Worksheet
This worksheet focuses on the properties of opposite angles in cyclic quadrilaterals and related circle theorems. It includes a range of questions from basic calculations to multi-step reasoning and real-world contexts.
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Opposite Angles: Problem Solving & Reasoning
Subject: MathematicsGrade: GCSE Higher
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Untitled Worksheet
Grade GCSE Higher
A
Introduction
Read the key concept carefully before attempting the questions. Remember, in a cyclic quadrilateral, opposite angles sum to 180°.
B
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the measure of an angle opposite a 65° angle in a cyclic quadrilateral.
[2 marks]2.
In a cyclic quadrilateral, one angle is 120°. What is the measure of its opposite angle?
[2 marks]3.
A cyclic quadrilateral has an angle of 85°. Find the opposite angle.
[2 marks]4.
Construct a quadrilateral with opposite angles measuring 70° and 110° on your grid.
[3 marks]C
Targeted Practice
Solve these problems to deepen your understanding.
1.
The angles of a cyclic quadrilateral are in the ratio 1:2:3:4. Find the measures of all its angles.
[3 marks]2.
In a circle, a quadrilateral inscribed has an angle of 75°. What is the measure of its opposite angle?
[2 marks]3.
A cyclic quadrilateral has three angles measuring 50°, 70°, and 110°. Find the fourth angle.
[2 marks]4.
Explain why the opposite angles of a cyclic quadrilateral are supplementary.
[3 marks]D
Real-world Applications
Apply your knowledge to solve these contextual problems.
1.
A circular table has a quadrilateral painted on its surface with opposite angles marked as 100° and 80°. If the quadrilateral is inscribed in the circle, what are the measures of the other two angles?
[3 marks]2.
A CCTV camera is installed at the center of a circular plaza. A cyclic quadrilateral is inscribed in the plaza with two opposite angles of 45°. Calculate the measures of the other two angles.
[3 marks]E
Challenge & Extension
Tackle these advanced problems to extend your understanding.
1.
Prove that in any cyclic quadrilateral, the sum of the measures of a pair of opposite angles is 180°, using circle theorems.
[4 marks]2.
Given a cyclic quadrilateral with three angles measuring 85°, 95°, and 60°, determine the measure of the fourth angle.
[2 marks]F
Mixed Review & Error Analysis
Identify and correct the mistakes in these statements.
1.
Statement: Opposite angles in a cyclic quadrilateral are always equal.
Identify the mistake and correct it.
[3 marks]2.
A student claims that if two angles in a cyclic quadrilateral are 110° and 70°, the other two must be 70° and 110°. Is this correct? Explain.
[3 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet