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=8x−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:

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°

answer: the correct one is a

step-by-step explanation:

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°