Question

question 1 of 25
in the figure below, ∠abd measures 37°. what is the measure of ∠abc?
a. 47°
b. 64°
c. 74°
d. 37°

Explanation:

Step1: Identify right angles and congruent segments

From the figure, \( \angle BAC \) and \( \angle BCD \) are right angles (\( 90^\circ \)), and segments \( CD \) and \( DA \) (or related segments) suggest a rectangle or congruent triangles. Also, \( BD \) is a bisector or creates congruent angles? Wait, actually, since \( \angle ABD = 37^\circ \), and \( \angle ABC \) is related to \( \angle ABD \) in a right angle context? Wait, no—wait, the figure has \( BC \) and \( BA \) as vertical and horizontal, \( CD \) and \( DA \) with right angles. Wait, maybe \( \triangle ABD \) and \( \triangle CBD \) are congruent? So \( \angle ABD = \angle CBD = 37^\circ \), so \( \angle ABC = \angle ABD + \angle CBD = 37^\circ + 37^\circ = 74^\circ \)? Wait, no, wait—wait, \( \angle ABC \) is composed of \( \angle ABD \) and \( \angle DBC \). If \( BD \) is a line that splits \( \angle ABC \) into two equal parts? Wait, no, the segments \( CD \) and \( DA \) are marked equal? Wait, the figure shows \( CD \) and \( DA \) with tick marks, so maybe \( CD = DA \), and \( BC \) and \( BA \) are perpendicular. So \( \angle ABD = 37^\circ \), and since \( \triangle ABD \) and \( \triangle CBD \) are congruent (right triangles with equal legs? \( CD = DA \), \( BC = BA \)?), so \( \angle CBD = \angle ABD = 37^\circ \). Then \( \angle ABC = \angle ABD + \angle CBD = 37 + 37 = 74^\circ \).

Step2: Calculate \( \angle ABC \)

Given \( \angle ABD = 37^\circ \), and if \( \angle CBD = \angle ABD \) (due to congruent triangles or angle bisector, but from the figure, the segments suggest congruent triangles), then \( \angle ABC = \angle ABD + \angle CBD = 37^\circ + 37^\circ = 74^\circ \).

Answer:

C. \( 74^\circ \)