Question

In circle BB, m, arc, D, C, equals, 109, degreesm
DC
⌢
=109
∘
. Solve for xx if m, angle, D, B, C, equals, left parenthesis, 9, x, plus, 24, right parenthesis, degreesm∠DBC=(9x+24)
∘
. If necessary, round your answer to the nearest tenth.
D
C
B
Answer
Attempt 2 out of 2

Answer 1

Arc DC measures 109°, and angle DBC is an inscribed angle that intercepts arc DC, so

m∠DBC = 1/2 · m(arc DC) = 109/2 = 54.5°.

Set 9x + 24 = 54.5:
9x = 54.5 − 24 = 30.5
x = 30.5/9 = 61/18 ≈ 3.3889.

Rounded to the nearest tenth: x = 3.4.