Question

Quadrilateral ABCD is inscribed in this circle.

What is the measure of ZA?
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Answer 1

Given:

ABCD is a cyclic quadrilateral.

m∠C = 43°

To find:

The measure of ∠A.

Solution:

In cylic quadrilateral, opposite angles are supplementary.

⇒ m∠A + m∠C = 180°

⇒ m∠A + 43° = 180°

Subtract 43° from both sides.

⇒ m∠A + 43° - 43° = 180° - 43°

⇒ m∠A = 137°

The measure of ∠A is 137°.