Question

question 26 of 45 given that △abc≅△def, what is the measure of ∠d? a. 39° b. 90° c. 47° d. 94°

Explanation:

Step1: Recall property of congruent triangles

Corresponding angles of congruent triangles are equal. Since $\triangle ABC\cong\triangle DEF$, $\angle D$ corresponds to $\angle A$.

Step2: Calculate $\angle A$

In $\triangle ABC$, use the angle - sum property of a triangle ($\angle A+\angle B+\angle C = 180^{\circ}$). Given $\angle B = 94^{\circ}$ and $\angle C=39^{\circ}$, then $\angle A=180^{\circ}-\angle B - \angle C=180^{\circ}-94^{\circ}-39^{\circ}=47^{\circ}$.

Step3: Find $\angle D$

Since $\angle D=\angle A$, $\angle D = 47^{\circ}$.

Answer:

C. $47^{\circ}$