Quadrilateral abcd is inscribed in a circle. what is the measure of angle a?

M∠A = 133°.

Opposite angles in an inscribed quadrilateral are supplementary, so we have

(4x+5)+(x+15) = 180

Combining like terms gives us
5x + 20 = 180

Subtract 20 from both sides:
5x+20 - 20 = 180 - 20
5x = 160

Divide both sides by 5:
5x/5 = 160/5
x = 32

Substitute this into our expression for ∠A:
4(32) + 5
128 + 5
133