Question

А Calculator Quadrilateral ABCD is inscribed in this circle. (2x - 40) 116 B. What is the measure of angle A? Enter your answer in the box. ( Will Mark Brainliest if answered correctly).​

Answer 1

Answer:

x = 64°

∠A = 88°

∠C = 92°

Step-by-step explanation:

This is a cyclic quadrilateral, since every vertex of the quadrilateral touches the circumference of the circle.

The opposite angles in a cyclic quadrilateral add up to 180°

∠B is opposite to ∠D

⇒ ∠B + ∠D = 180

⇒ 116 + x = 180

⇒ x = 180 - 116

⇒ x = 64°

If x = 64°, then

⇒ ∠A = (2 x 64) - 40

⇒ ∠A = 88°

∠A is opposite to ∠C

⇒ ∠A + ∠C = 180

⇒ 88 + ∠C = 180

⇒ ∠C = 180 - 88

⇒ ∠C = 92°