Question

guided practice find m∠abc 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. a. 102° b. 14° c. 54° d. 78° diagram: straight line a---b---d with arrows at a (up) and d (down), ray b---c with arrow at c. angles: ∠abc = (4x + 22)°, ∠cbd = (8x - 10)°

Explanation:

Step1: Recognize linear pair

Angles \( \angle ABC \) and \( \angle DBC \) form a linear pair, so their sum is \( 180^\circ \). Thus, \( (4x + 22) + (8x - 10) = 180 \).

Step2: Solve for \( x \)

Combine like terms: \( 12x + 12 = 180 \). Subtract 12: \( 12x = 168 \). Divide by 12: \( x = 14 \).

Step3: Find \( m\angle ABC \)

Substitute \( x = 14 \) into \( 4x + 22 \): \( 4(14) + 22 = 56 + 22 = 78 \).

Answer:

\( 78^\circ \) (Option D)