Question 1: In a cyclic quadrilateral, two opposite angles measure 75° and 110°. Calculate the measures of the other two opposite angles.

Answer: 95°, 95°

Question 2: Explain why the opposite angles in a cyclic quadrilateral always add up to 180°.

Answer: In a cyclic quadrilateral, all vertices lie on a circle. The opposite angles subtend supplementary arcs, so their measures sum to 180°.

Question 3: A quadrilateral inscribed in a circle has one angle measuring 85°. Find the measure of its opposite angle.

Answer: 95°

Question 4: Construct a cyclic quadrilateral with two opposite angles measuring 60° and 120°. What are the measures of the other two angles?

Answer: 60°, 120°

Question 5: In a real-world scenario, a circular track has a quadrilateral marking on it. If one pair of opposite angles measures 80° and 100°, what are the measures of the other two opposite angles?

Answer: 80°, 100°

Question 6: A cyclic quadrilateral has three angles measuring 65°, 85°, and 90°. Find the measure of the fourth angle.

Answer: 70°

Question 7: A student claims that opposite angles in a cyclic quadrilateral can be any measure. Is this statement true or false? Explain your reasoning.

Answer: False. Opposite angles in a cyclic quadrilateral always add up to 180°.

Question 8: Given a cyclic quadrilateral where one angle is 100°, and its opposite angle is unknown, determine the measure of the opposite angle.

Answer: 80°

Question 9: A quadrilateral inscribed in a circle has two opposite angles measuring 50° and 130°. What are the measures of the other two opposite angles?

Answer: 50°, 130°

Question 10: Identify and correct the mistake in this reasoning: 'Opposite angles in a cyclic quadrilateral always measure 90°.'

Answer: Incorrect. Opposite angles sum to 180°, but are not necessarily 90° each.