Question

if ( mangle qrt = mangle srt = 58^{circ} ) and ( st = 5 ), what is ( qt )?
( qt=square )

Explanation:

Step1: Apply the Angle - Angle - Side (AAS) Congruence Theorem

Since \( \angle Q = \angle S=90^{\circ}\), \( \angle QRT=\angle SRT = 58^{\circ}\), and \(RT = RT\) (common side). By AAS congruence, \(\triangle QRT\cong\triangle SRT\).

Step2: Use the property of congruent triangles

If two triangles \(\triangle QRT\) and \(\triangle SRT\) are congruent, then their corresponding sides are equal. That is, \(QT = ST\).

Answer:

\(5\)