Question

Given \qquad m \angle aoc = 108^\circm∠aoc=108 ​∘ ​​ space, m, angle, a, o, c, equals, 108, degree \qquad m \angle aob = 3x + 4^\circm∠aob=3x+4 ​∘ ​​ space, m, angle, a, o, b, equals, 3, x, plus, 4, degree \qquad m \angle boc = 8x - 28^\circm∠boc=8x−28 ​∘ ​​ space, m, angle, b, o, c, equals, 8, x, minus, 28, degree find m\angle aob∠aob, angle, a, o,

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Answer 1

Explanation:

Given the following angle

We want to find angle AOB

∠AOC = 108°

∠AOB = 3x+4

∠BOC =8x−28 ​

Check attachment for understanding

From the attachment, we notice that the sum of angle AOB and angle BOC equals to angle AOC.

∠AOB + ∠BOC = ∠AOC

3x + 4 + 8x —28 = 108

3x + 8x + 4—28 = 108

11x — 24 = 108

11x = 108 + 24

11x = 132

x = 132/11

x = 12°

∠AOB = 3x+4

∠AOB = 3(12) + 4

∠AOB = 36+4

∠AOB = 40°

Extra

∠BOC = 8x−28

∠BOC = 8(12)−28

∠BOC = 96−28

∠BOC = 68°