Quadrilateral ABCD is inscribed in this circle.

What is the measure of ∠A ?

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The measure of ∠A is 137°.

Solution:

Given data:

Angle A = 43°

A quadrilateral inscribed in a circle is called cyclic quadrilateral.

∠A and ∠C are opposite angles in a cyclic quadrilateral.

In cyclic quadrilateral, opposite angles are supplementary.

⇒ m∠A + m∠C = 180°

⇒ 43° + m∠A = 180°

Subtract 43° from both sides of the equation, we get

⇒ m∠A = 137°

Hence the measure of ∠A is 137°.

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step-by-step explanation:

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