Question

if rs = ru = 71 and m∠rtu = 65°, what is m∠stu?
m∠stu = □°
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Explanation:

Step1: Identify congruent triangles

Since \( RS = RU = 71 \) and \( \angle RST=\angle RUT = 90^\circ \) (right angles), and \( RT \) is common to both \( \triangle RST \) and \( \triangle RUT \), by the Hypotenuse - Leg (HL) congruence criterion, \( \triangle RST\cong\triangle RUT \). This implies that \( \angle RTS=\angle RTU \). Given \( m\angle RTU = 65^\circ \), so \( m\angle RTS=65^\circ \).

Step2: Calculate \( m\angle STU \)

We know that \( \angle STU=\angle RTS+\angle RTU \) (since \( \angle STU \) is composed of \( \angle RTS \) and \( \angle RTU \)). Substituting the values of \( \angle RTS \) and \( \angle RTU \), we get \( m\angle STU=65^\circ + 65^\circ=130^\circ \).

Answer:

\( 130 \)