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°.
