Opposite Angles: Challenge & Extension
Mathematics
Grade 7
13 questions
~26 mins
1 views0 downloads
About This Worksheet
A worksheet exploring Opposite Angles in Cyclic Quadrilaterals, including practice, reasoning, real-world applications, and extension questions for Grade 7 students.
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Opposite Angles: Challenge & Extension
Subject: MathematicsGrade: Grade 7
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Untitled Worksheet
Grade Grade 7
A
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
In a cyclic quadrilateral, angle A measures 70°. What is the measure of the opposite angle C?
[2 marks]2.
If two opposite angles of a cyclic quadrilateral are both 85°, what is the measure of each of the other two opposite angles?
[3 marks]3.
A cyclic quadrilateral has one pair of opposite angles measuring 60° and 120°. Find the other two opposite angles.
[3 marks]4.
Construct a cyclic quadrilateral where one opposite angle is 75° and the adjacent angle is 105°. Use the grid to draw and verify the angles.
[4 marks]5.
Explain why the opposite angles of a cyclic quadrilateral are supplementary. Provide a brief reasoning.
[3 marks]B
Problem Solving & Reasoning
Answer the following multi-step problems. Show detailed working.
1.
A quadrilateral inscribed in a circle has three angles measuring 65°, 85°, and 90°. Find the measure of the fourth angle. Justify your answer using the Opposite Angles Theorem.
[4 marks]2.
Two opposite angles in a cyclic quadrilateral measure 100° and 80°. One of the remaining angles is 70°. Find the measure of the last angle and explain your reasoning.
[4 marks]C
Real-world Applications
Apply your understanding to solve real-world inspired problems.
1.
A circular table has four seats arranged around it, each seat forming an inscribed angle with the table's center. If one of the angles is 75°, what is the measure of the opposite angle to this seat? Use reasoning based on Opposite Angles in cyclic quadrilaterals.
[3 marks]D
Challenge & Extension
Attempt these more advanced problems to extend your understanding.
1.
In a cyclic quadrilateral, the measure of an angle is 40°. Its opposite angle is unknown. If the sum of these two angles equals the measure of one of the other angles in the quadrilateral, what is the measure of that third angle? Show your reasoning.
[4 marks]2.
Construct a cyclic quadrilateral on the grid where one pair of opposite angles are both 110°, and verify the other two angles using the Opposite Angles Theorem.
[4 marks]E
Mixed Review
Answer these diverse questions to consolidate your understanding.
1.
Two angles in a cyclic quadrilateral measure 55° and 125°. Find the measures of their opposite angles.
[2 marks]2.
Explain a common mistake students make when calculating opposite angles and how to avoid it.
[3 marks]F
Error Analysis
Review the following scenario and identify the mistake. Correct it and explain why.
1.
A student claims that in a cyclic quadrilateral, if one angle measures 85°, then its opposite angle must also be 85°. Is this correct? Explain your reasoning and correct the misconception if necessary.
[3 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet