Question

question 22 of 25 in the figure below, ∠abd measures 41°. what is the measure of ∠abc? a. 82° b. 72° c. 51° d. 41°

Explanation:

Step1: Identify congruent triangles

Triangles $\triangle BCD$ and $\triangle BAD$ are congruent by Hypotenuse - Leg (HL) congruence criterion (right - angled triangles with equal hypotenuses and one equal leg).

Step2: Determine angle relationship

Since $\triangle BCD\cong\triangle BAD$, $\angle ABD=\angle CBD$.

Step3: Calculate $\angle ABC$

$\angle ABC=\angle ABD + \angle CBD$. Given $\angle ABD = 41^{\circ}$, then $\angle ABC=41^{\circ}+41^{\circ}=82^{\circ}$.

Answer:

A. $82^{\circ}$