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.

Answer 1

Arc DC measures 109°, so inscribed angle ∠DBC = 1/2·arc DC = 109/2 = 54.5°.
Set 9x + 24 = 54.5:
9x = 30.5 → x = 30.5/9 = 61/18 ≈ 3.4.

Answer: x = 61/18 ≈ 3.4.