Question

in △qrs, \\(overline{rs} \cong overline{qr}\\) and \\(m\angle q = 46^\circ\\). find \\(m\angle s\\).

Explanation:

Step1: Identify triangle type

$\triangle QRS$ is isosceles with $\overline{RS} \cong \overline{QR}$.

Step2: Match congruent sides to angles

In isosceles triangles, angles opposite congruent sides are congruent. $\angle Q$ is opposite $\overline{RS}$, $\angle S$ is opposite $\overline{QR}$.

Step3: State measure of $\angle S$

Since $\angle Q \cong \angle S$, $\text{m}\angle S = \text{m}\angle Q$.
<Expression>$\text{m}\angle S = 46^\circ$</Expression>

Answer:

$\boldsymbol{46^\circ}$