Question

7 fill in the blank 1 point in the figure below, angle abd measures 32 degrees. what is the measure of angle abc? choose your answer... choose your answer... 42 degrees 74 degrees 64 degrees 32 degrees

Explanation:

Step1: Identify congruent triangles

Triangles \(ABD\) and \(CBD\) are congruent (by Hypotenuse - Leg congruence for right - angled triangles, since \(BD = BD\) (common side), \(AD = CD\) (given), \(\angle BAD=\angle BCD = 90^{\circ}\)).

Step2: Use angle - congruence property

Since \(\triangle ABD\cong\triangle CBD\), \(\angle ABD=\angle CBD\). Given \(\angle ABD = 32^{\circ}\), then \(\angle ABC=\angle ABD+\angle CBD\).

Step3: Calculate \(\angle ABC\)

Substitute \(\angle ABD=\angle CBD = 32^{\circ}\) into the formula \(\angle ABC=\angle ABD+\angle CBD\). So \(\angle ABC=32^{\circ}+32^{\circ}\).

Answer:

\(64\) degrees