Question

if (overline{ps}congoverline{rs}) and (mangle pqs = 43^{circ}), what is (mangle rqs)?
(mangle rqs=square^{circ})

Explanation:

Step1: Use the Hypotenuse - Leg (HL) Congruence Theorem

Since \( \overline{PS}\cong\overline{RS}\), \( \overline{SQ}\cong\overline{SQ}\) (common side), and \( \angle SPQ=\angle SRQ = 90^{\circ}\), by the HL theorem, \( \triangle SPQ\cong\triangle SRQ\).

Step2: Use the property of congruent triangles

If \( \triangle SPQ\cong\triangle SRQ\), then \( \angle PQS=\angle RQS\) (corresponding parts of congruent triangles are congruent).
Given \( m\angle PQS = 43^{\circ}\), so \( m\angle RQS=43^{\circ}\).

Answer:

\(43\)