Equation practice with angle addition

Question

Given:
m∠AOCm, angle, A, O, C is a straight angle.
\qquad m \angle BOC = 6x + 29^\circm∠BOC=6x+29
∘
m, angle, B, O, C, equals, 6, x, plus, 29, degrees
\qquad m \angle AOB = 3x + 124^\circm∠AOB=3x+124
∘

Find m\angle BOCm∠BOCm, angle, B, O, C:

B
_____________/_______________C
O

Answer 1

since AOC is a straight line,
AOB+BOC = 180°
Thus,
3x+124 + 6x+29 = 180
9x + 153 = 180
9x = 27
x = 3
BOC = 6x+29 = 47°

Answer 2

m∠BOC=47

Answer 3

m∠AOCm, angle, A, O, C is a straight angle.
\qquad m \angle BOC = 6x + 29^\circm∠BOC=6x+29
∘
m, angle, B, O, C, equals, 6, x, plus, 29, degrees
\qquad m \angle AOB = 3x + 124^\circm∠AOB=3x+124
∘
m, angle, A, O, B, equals, 3, x, plus, 124, degrees
Find m\angle BOCm∠BOCm, angle, B, O, C:

Answer 4

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