Question

q. what is the measure of ∠s?

Explanation:

Step1: Use the triangle angle - sum property

The sum of interior angles of a triangle is \(180^{\circ}\). So, \(x + 3x+\angle S=180^{\circ}\).

Step2: Use the property of isosceles triangle

Since two sides of \(\triangle RSI\) are equal (marked with the same symbol), \(\angle R=\angle S=x\).

Step3: Solve the equation

Substitute \(\angle S = x\) into \(x + 3x+\angle S=180^{\circ}\), we get \(x+3x + x=180^{\circ}\), i.e., \(5x = 180^{\circ}\). Then \(x=\frac{180^{\circ}}{5}=36^{\circ}\). So \(\angle S=x = 36^{\circ}\).

Answer:

\(36^{\circ}\)