Question 33 of 50beginner🔧 ApplyShort Answer2 marks

ABCD is a cyclic quadrilateral inscribed in a circle. If ∠\angleA measures 75°, what is the measure of ∠\angleC? If ∠\angleB measures 110°, what is the measure of ∠\angleD?

Correct Answer

(angle C) 105°

(angle D) 70°

Exercise: END-OF-CHAPTER EXERCISES | Q: 7 | (Page 23)
For More Understanding

Explanation

ABCD is a cyclic quadrilateral, and a key property of such a quadrilateral is that the opposite angles add up to 180°. This means ∠A + ∠C = 180° and ∠B + ∠D = 180°.

For the first part, we are given ∠A = 75°. To find ∠C, we subtract ∠A from 180°. Thus, ∠C = 180° - 75° = 105°.

For the second part, we are given ∠B = 110°. To find ∠D, we subtract ∠B from 180°. Thus, ∠D = 180° - 110° = 70°.

Solution Steps

  1. Step 1: Use the property that opposite angles of a cyclic quadrilateral add up to 180°.

  2. Step 2: Calculate angle C: 180° - 75° = 105°.

  3. Step 3: Calculate angle D: 180° - 110° = 70°.

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