Answer: The answer is 137°.
Step-by-step explanation: Given that the quadrilateral ABCD is inscribed in a circle, where measure of angle C is 43°. We are to find the measure of ∠A.
Since the quadrilateral ABCD is inscribed in a circle, so it will be a cyclic quadrilateral. Also, the sum of opposite angles of a cyclic quadrilateral is 180°.
Therefore, we have
[tex]\angle A+\angle C=180^\circ\\\\\Rightarrow \angle A+43^\circ=180^\circ\\\\\Rightarrow \angle A=180^\circ-43^\circ\\\\\Rightarrow \angle A=137^\circ.[/tex]
Thus, the required answer is 137°.
