Question

Given \qquad m \angle AOC = 108^\circm∠AOC=108 ∘ m, angle, A, O, C, equals, 108, degrees \qquad m \angle AOB = 3x + 4^\circm∠AOB=3x+4 ∘ m, angle, A, O, B, equals, 3, x, plus, 4, degrees \qquad m \angle BOC = 8x - 28^\circm∠BOC=8x−28 ∘ m, angle, B, O, C, equals, 8, x, minus, 28, degrees Find m\angle AOBm∠AOBm, angle, A, O, B:

Answer 1

40°

Step-by-step explanation:

Given the following

∠AOC = 108°

∠AOB = 3x + 4°

∠BOC = 8x - 28

∠AOC = ∠AOB+∠BOC

108 = 3x+4+8x-28

108 = 11x-24

11x = 108+24

11x = 132

x = 132/11

x = 12

Next is to get ∠AOB. Recall that:

∠AOB = 3x+4

∠AOB = 3(12)+4

∠AOB = 36+4

∠AOB = 40°

Hence the measure of ∠AOB is 40°