Question

1. $m\angle dba = 4x + 10$, $m\angle cbd = -8 + 9x$, and $m\angle cba = 158^\circ$. find $m\angle cbd$.

a) $-2^\circ$
b) $63^\circ$
c) $12^\circ$
d) $100^\circ$

Explanation:

Step1: Set up the angle addition equation

We know that \( m\angle CBA = m\angle DBA + m\angle CBD \). Substituting the given expressions: \( 158 = (4x + 10) + (-8 + 9x) \).

Step2: Solve for \( x \)

Combine like terms: \( 158 = 13x + 2 \). Subtract 2 from both sides: \( 156 = 13x \). Divide by 13: \( x = 12 \).

Step3: Find \( m\angle CBD \)

Substitute \( x = 12 \) into \( m\angle CBD = -8 + 9x \): \( -8 + 9(12) = -8 + 108 = 100 \).

Answer:

D) \( 100^\circ \)