The measure of angle A is 88°.
Solution:
Given data:
∠A = (2x – 40)°, m∠B = 116° and ∠D = x°
A quadrilateral inscribed in a circle is called cyclic quadrilateral.
∠B and ∠D are opposite angles in a cyclic quadrilateral.
In cyclic quadrilateral, opposite angles are supplementary.
⇒ m∠B+ m∠D = 180°
⇒ 116° + x = 180
°
Subtract 116° from both sides of the equation, we get
⇒ x = 64
°
To find the measure of angle A:
m∠A = (2x – 40)°
= 2(64°) – 40°
m∠A = 88°
Hence the measure of angle A is 88°.
