Question

if sv = uv = 1 and m∠stv = 67°, what is m∠stu?

m∠stu = °
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Explanation:

Step1: Identify Right Triangles

Triangles \( \triangle VST \) and \( \triangle VUT \) are right triangles (since \( \angle VST = 90^\circ \) and \( \angle VUT = 90^\circ \)). Given \( SV = UV = 1 \) and \( VT \) is common to both triangles, by the Hypotenuse - Leg (HL) congruence criterion, \( \triangle VST \cong \triangle VUT \).

Step2: Use Congruence to Find Angles

Since \( \triangle VST \cong \triangle VUT \), \( \angle STV=\angle UTV = 67^\circ \). To find \( \angle STU \), we note that \( \angle STU=\angle STV+\angle UTV \).

Step3: Calculate \( \angle STU \)

Substitute the values of \( \angle STV \) and \( \angle UTV \) into the formula: \( \angle STU = 67^\circ+ 67^\circ=134^\circ \).

Answer:

\( 134 \)