Quadrilateral ABCD is inscribed in this circle.What is the measure of angle A?Enter your answer in the box.°
Accepted Solution
A:
Answer:m∠A = 116°Step-by-step explanation:For better understanding of the solution, see the attached figure of the problem :
The quadrilateral ABCD is inscribed in a circle, Thus the quadrilateral ABCD is a cyclic quadrilateral.
Also, Sum of opposite angles of a cyclic quadrilateral is supplementary.
Now, m∠A = (x - 36)°, m∠B = 28° and m∠D = x°
But, since the sum of opposite angles is 180°
⇒ 28° + x° = 180°
⇒ x = 180 - 28
⇒ x = 152
So, m∠A = (x - 36)°
⇒ m∠A = (152 - 36)°
⇒ m∠A = 116°