Question

what is m∠tsu? m∠tsu = °

Explanation:

Step1: Identify congruent right - triangles

In right - triangles $\triangle RSU$ and $\triangle TSU$, $SU = SU$ (common side), $RU = TU=10$, and $\angle R=\angle T = 90^{\circ}$. By the Hypotenuse - Leg (HL) congruence criterion, $\triangle RSU\cong\triangle TSU$.

Step2: Use congruent - angle property

Since $\triangle RSU\cong\triangle TSU$, corresponding angles are equal. So, $\angle RSU=\angle TSU$.

Step3: Calculate $\angle TSU$

Given $\angle RST = 47^{\circ}$, and $\angle RST=\angle RSU+\angle TSU$. Since $\angle RSU=\angle TSU$, then $\angle TSU=\frac{1}{2}\angle RST$.
$\angle TSU=\frac{1}{2}\times47^{\circ}=23.5^{\circ}$

Answer:

$23.5$