Question

question 33 of 50
in the graphic below, the measure of angle abc is:
triangle with right angle at d, angle at a is 37 degrees, b on the base extended to c
options: 90°, 37°, 143°, 127°

Explanation:

Step1: Analyze triangle ADB

Triangle \( ADB \) is a right triangle with \( \angle D = 90^\circ \) and \( \angle A = 37^\circ \). The sum of angles in a triangle is \( 180^\circ \), so \( \angle ABD = 180^\circ - 90^\circ - 37^\circ = 53^\circ \).

Step2: Find angle ABC

Angles \( \angle ABD \) and \( \angle ABC \) are supplementary (they form a linear pair), so \( \angle ABC = 180^\circ - \angle ABD = 180^\circ - 53^\circ = 127^\circ \)? Wait, no, wait. Wait, maybe I made a mistake. Wait, let's recheck. Wait, in triangle \( ADB \), right-angled at \( D \), so \( \angle A + \angle ABD = 90^\circ \) (because in a right triangle, the two acute angles are complementary). So \( \angle ABD = 90^\circ - 37^\circ = 53^\circ \). Then \( \angle ABC \) and \( \angle ABD \) are supplementary, so \( \angle ABC = 180^\circ - 53^\circ = 127^\circ \)? Wait, but the options have 127? Wait, no, the options are 90, 37, 143, 127. Wait, maybe I messed up. Wait, no, let's see: \( \angle A = 37^\circ \), \( \angle D = 90^\circ \), so \( \angle ABD = 90 - 37 = 53^\circ \). Then \( \angle ABC = 180 - 53 = 127^\circ \). Wait, but maybe the triangle is different. Wait, maybe \( \angle A = 37^\circ \), and \( \angle D \) is right, so \( \angle ABD = 53^\circ \), so \( \angle ABC = 180 - 53 = 127^\circ \). Wait, but let's check again. Wait, maybe the angle at \( A \) is 37, so \( \angle ABD = 90 - 37 = 53 \), so \( \angle ABC = 180 - 53 = 127 \). So the answer is 127.

Answer:

\( 127^\circ \) (corresponding to the option with 127°)