Question

What is the arc measure of AD in degrees?

Answer 1

∠APD, ∠DPC, ∠CPB are supplementary angles (angles whose sum is 180°). ∠DPC is right angle (angle whose measurement 90°)

Make an expression based on the information above, then solve for x
∠APD + ∠DPC + ∠CPB = 180°
7x + 1 + 90 + 9x - 7 = 180

add like terms
7x + 9x + 1 + 90 - 7 = 180
16x + 84 = 180
16x = 180 - 84
16x = 96
 x = 96/16
 x = 6

The value of x is 6, substitute this value to APD's algebraic expression
∠APD = 7x + 1
∠APD = 7(6) + 1
∠APD = 42 + 1
∠APD = 43

The measurement of ∠APD is 43°