Question

question 9 of 25
in the figure below, ∠abd measures 37°. what is the measure of ∠abc?

a. 74°
b. 37°
c. 54°
d. 47°

Explanation:

Step1: Identify figure properties

The figure shows that $BC = BA$, $CD = AD$, and $\angle BCD = \angle BAD = 90^\circ$, so $BD$ is the angle bisector of $\angle ABC$.

Step2: Relate angles

Since $BD$ bisects $\angle ABC$, $\angle ABC = 2\times\angle ABD$.
$\angle ABC = 2\times37^\circ$

Answer:

A. $74^\circ$