Question

$\triangle abc \sim \triangle uts$. what are $m\angle c$ and $m\angle u$?
$m\angle c = \square^{\circ}$
$m\angle u = \square^{\circ}$

Explanation:

Step1: Identify congruent angles

Since $\triangle ABC \sim \triangle UTS$, corresponding angles are equal:
$\angle A \cong \angle U$, $\angle B \cong \angle T$, $\angle C \cong \angle S$

Step2: Find $m\angle C$

$\angle C$ corresponds to $\angle S$, so $m\angle C = m\angle S = 39^\circ$

Step3: Find $m\angle U$

$\angle U$ corresponds to $\angle A$, so $m\angle U = m\angle A = 105^\circ$

Answer:

$m\angle C = 39^\circ$
$m\angle U = 105^\circ$