Quadrilateral ABCD is inscribed in this
circle.
What is the measure of angle A?
Enter your answer in the box.

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°.

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step-by-step explanation: