Question

guided practice
when finding an angle measure, find x first. then, use the following steps.

1. substitute the value for x into the expression representing the angle.
2. simplify the expression.

find ( mangle abc )
a. ( 32^circ )
b. ( 48^circ )
c. ( 96^circ )
d. ( 42^circ )

Explanation:

Step1: Identify angle relationship

Since \( \angle ABD \) is a right angle (\( 90^\circ \)), \( \angle ABC + \angle CBD = 90^\circ \). So, \( 8x + (5x + 12) = 90 \).

Step2: Solve for \( x \)

Combine like terms: \( 13x + 12 = 90 \). Subtract 12: \( 13x = 78 \). Divide by 13: \( x = 6 \).

Step3: Find \( m\angle ABC \)

Substitute \( x = 6 \) into \( 8x \): \( 8(6) = 48 \).

Answer:

\( 48^\circ \) (Option B. \( 48^\circ \))