Question

Help! Find the measure of the arc or angle indicated.

Answer 1

m<QDC = 77

Explanation:

First we need to generate an equation in order to find the value of x.

Thus:

m<QDC = ½(Arc QBC) => Inscribed Angles Theorem)

5x + 17 = ½(4x - 6 + 9x + 4)

5x + 17 = ½(13x - 2)

Multiply both sides by 2

2(5x + 17) = 13x - 2

10x + 34 = 13x - 2

Collect like terms

10x - 13x = -34 - 2

-3x = -36

Divide both sides by -3

-3x/-3 = -36/-3

x = 12

Find m<QDC:

m<QDC = 5x + 17

Plug in the value of x

m<QDC = 5(12) + 17 = 70 + 17

m<QDC = 77