Given \qquad m \angle AOC = 96^\circm∠AOC=96 ∘ m, angle, A, O, C, equals, 96, degrees \qquad m \angle BOC = 8x - 67^\circm∠BOC=8
x−67 ∘ m, angle, B, O, C, equals, 8, x, minus, 67, degrees \qquad m \angle AOB = 9x - 75^\circm∠AOB=9x−75 ∘ m, angle, A, O, B, equals, 9, x, minus, 75, degrees Find m\angle BOCm∠BOCm, angle, B, O, C:
2 answers:
Answer:
124.2°
Step-by-step explanation:
Given
∠AOC=96°
∠BOC=8x−67°
∠AOB=9x−75°
We notice that the angles are all centred at point O.
Therefore,
∠AOC+∠BOC+∠AOB=360° (Sum of Angles at a point)
Substituting the values:
96°+8x−67°+9x−75°=360°
8x+9x=360+75+67-96
17x=406°
x=23.9°
Next we find ∠BOC
∠BOC=8x−67°
=(8 X 23.9)-67°
=191.2-67
=124.2°
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