Question

if sv = uv = 58 and m∠utv = 36°, what is m∠stu? m∠stu = °

Explanation:

Step1: Identify the property of angle bisector

Since \( SV = UV \) and \( \angle VUS = \angle VSS = 90^\circ \) (right angles), \( VT \) is the angle bisector of \( \angle STU \) (by the Angle - Bisector Theorem converse: if a point is equidistant from the sides of an angle, then it lies on the angle bisector).

Step2: Calculate \( m\angle STU \)

We know that \( m\angle UTV=36^\circ \), and since \( VT \) bisects \( \angle STU \), \( \angle STU = 2\times\angle UTV \).
So \( m\angle STU=2\times36^\circ = 72^\circ \).

Answer:

\( 72 \)