Question

question
in △rst, overline{st} cong overline{rs} and m∠r = 41°. find m∠s.

Explanation:

Step1: Identify the triangle type

Since \( \overline{ST}\cong\overline{RS}\), \(\triangle RST\) is an isosceles triangle. In an isosceles triangle, the base angles are equal. So, \(\angle T=\angle R = 41^{\circ}\).

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 \(m\angle R + m\angle S+m\angle T=180^{\circ}\).
Substitute \(m\angle R = 41^{\circ}\) and \(m\angle T = 41^{\circ}\) into the equation: \(41^{\circ}+x + 41^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

Combine like terms: \(x+82^{\circ}=180^{\circ}\).
Subtract \(82^{\circ}\) from both sides of the equation: \(x=180^{\circ}- 82^{\circ}\).
\(x = 98^{\circ}\).

Answer:

\(m\angle S = 98^{\circ}\)