Same Arc: Challenge & Extension
Mathematics
Year 9
11 questions
~22 mins
1 views0 downloads
About This Worksheet
A challenging worksheet exploring the concept of angles subtended by the same arc in a circle. Designed to develop procedural skills and higher-order reasoning for Year 9 students.
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Full preview • 11 questions
Same Arc: Challenge & Extension
Subject: MathematicsGrade: Year 9
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Untitled Worksheet
Grade Year 9
A
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
In a circle, two angles subtend the same arc. If one angle measures 65°, calculate the measure of the other angle.
[2 marks]2.
Construct a circle with two angles on the circumference measuring 40° and 70°, both subtending the same arc. Verify if they are subtended by the same arc.
[3 marks]3.
A circle has an inscribed triangle with angles 50°, 60°, and x°. If the angles at the circumference subtend the same arc, find x.
[3 marks]4.
Two angles are inscribed in a circle and both measure 55°. Are these angles subtended by the same arc? Explain your reasoning.
[3 marks]5.
In a circle, an angle of 80° is formed at the circumference. Find the measure of the angle at the center subtended by the same arc.
[2 marks]6.
Identify the common mistake in the following reasoning: 'Angles subtended by different arcs are equal.' Provide the correct statement.
[2 marks]7.
A chord subtends a 60° angle at the circumference. What is the measure of the angle subtended by the same chord at the opposite side of the circle?
[3 marks]8.
A circle has two points A and B on its circumference. An angle at point C on the circle subtends the same arc AB as angle at point D. If angle at C measures 45°, find the measure of angle at D.
[3 marks]9.
Explain why an angle measured at the center of a circle is twice any inscribed angle subtending the same arc.
[3 marks]10.
A certain inscribed angle in a circle measures 35°. Construct the corresponding central angle and explain the relationship.
[3 marks]11.
Challenge: In a circle, two angles at the circumference measure 50° and 70°, both subtending the same arc. Is this possible? Justify your answer.
[3 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet