Answer:
The measure of angle A = 133°
Explanation:
The sum of opposite angles of cyclic quadrilateral is 180°
From the figure we can see that,quadrilateral ABCD is inscribed in a circle.
<A + <C = 180°
To find the value of x
we have,
(4x + 5) + (x + 15) = 180
4x + 5 + x + 15 = 180
5x + 20 = 180
5x = 180 - 20 = 160
x = 160/5 = 32
To find the measure of angle
m<A = 4x + 5
x = 32
m<A = 4*32 + 5 = 128 + 5 = 133°
Therefore the measure of angle A = 133°