Question

question
in \\( \triangle q r s, \overline{s q} \cong \overline{r s} \\) and \\( \mathrm{m} \angle r=48^{\circ} \\). find \\( \mathrm{m} \angle s \\).

Explanation:

Step1: Identify the triangle type

Since $\overline{SQ}\cong\overline{RS}$, $\triangle QRS$ is an isosceles triangle. In an isosceles triangle, the base angles are equal. So $\angle Q=\angle R = 48^{\circ}$.

Step2: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is $180^{\circ}$. Let $m\angle S=x$. Then, by the triangle - angle sum theorem, $\angle Q+\angle R+\angle S = 180^{\circ}$. Substitute $\angle Q = 48^{\circ}$ and $\angle R = 48^{\circ}$ into the equation: $48^{\circ}+48^{\circ}+x=180^{\circ}$.

Step3: Solve for $x$

First, simplify the left - hand side of the equation: $96^{\circ}+x = 180^{\circ}$. Then, subtract $96^{\circ}$ from both sides: $x=180^{\circ}-96^{\circ}=84^{\circ}$.

Answer:

$m\angle S = 84^{\circ}$