Question

OA ⊥ OC start overline, O, A, end overline, \perp, start overline, O, C, end overline \qquad m \angle BOC = 6x - 6^\circm∠BOC=6x−6 ∘ m, angle, B, O, C, equals, 6, x, minus, 6, degrees \qquad m \angle AOB = 5x + 8^\circm∠AOB=5x+8 ∘ m, angle, A, O, B, equals, 5, x, plus, 8, degrees Find m\angle BOCm∠BOCm, angle, B, O, C:

Answer 1

Answer:

42 degrees.

Step-by-step explanation:

$\angle BOC+\angle AOB=90^\circ (Complementary Angles)\\6x - 6^\circ+5x + 8^\circ=90^\circ\\6x+5x-6^\circ+ 8^\circ=90^\circ\\11x+ 2^\circ=90^\circ\\11x=90^\circ-2^\circ\\11x=88^\circ\\ Divide both sides by 11\\x=8^\circ\\ Therefore:\\m\angle BOC=6x - 6^\circ\\=6(8) - 6^\circ\\=48-6\\=42^\circ$

The measure of angle BOC is 42 degrees.