Question

Triangle ABC is congruent to triangle DEF. Angle B is a right angle, and m∠C = 57°. What is m∠D? a33° b43° c52° d57°

Answer 1

Since ABC is congruen to DEF then their corresponding angles are congruent:

$\begin{gathered} m\angle A=m\angle D \\ m\angle B=m\angle E \\ m\angle C=m\angle F \end{gathered}$

Since interior angles of a triangle add up to 180, we have

$\begin{gathered} m\angle A+m\angle B+m\angle C=180 \\ m\angle A+90+57=180 \end{gathered}$

Which gives

$\begin{gathered} m\angle A+147=180 \\ \text{then} \\ m\angle A=33 \end{gathered}$

From our result form above, we know that

$m\angle A=m\angle D=33$

So, the answer is option A