In right triangle $△PQR$, the angle bisector of $\angle PQR$ is $QE$. If $m\angle PQE=20°$, what is the measure of $\angle PQR$?

• A. $20°$
• B. $90°$
• C. $40°$
• D. $60°$

Answer: (C)

Verified step by step guidance

1. Identify the given elements: triangle \( \triangle PQR \) is a right triangle, and \( Q E \) is the angle bisector of angle \( \angle PQR \). This means \( \angle PQR \) is split into two equal angles by the segment \( Q E \).
2. Since \( Q E \) bisects \( \angle PQR \), the two angles formed at \( Q \) are equal. Given that \( m\angle PQE = 20^\circ \), it follows that \( m\angle EQ R = 20^\circ \) as well.
3. Therefore, the entire angle \( \angle PQR \) is the sum of these two equal angles: \( m\angle PQR = m\angle PQE + m\angle EQR = 20^\circ + 20^\circ \).
4. Recall that \( \triangle PQR \) is a right triangle, so one of its angles is \( 90^\circ \). Since \( \angle PQR \) is the angle being bisected, it must be less than \( 90^\circ \).
5. Conclude that \( m\angle PQR = 40^\circ \) by adding the two equal parts, which matches the sum of the two \( 20^\circ \) angles formed by the bisector.