Question

what is the value of y? y =

Explanation:

Step1: Determine the type of triangle

Since two sides of the triangle are equal (marked with the same tick), triangle \(TSR\) is an isosceles triangle. In an isosceles triangle, the base - angles are equal. So, \(\angle T=\angle S = 40^{\circ}\).

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(\angle R=y\). Then, using the formula \(\angle T+\angle S+\angle R = 180^{\circ}\).
Substitute \(\angle T = 40^{\circ}\) and \(\angle S=40^{\circ}\) into the formula:
\(40^{\circ}+40^{\circ}+y=180^{\circ}\).
Simplify the left - hand side: \(80^{\circ}+y = 180^{\circ}\).
Subtract \(80^{\circ}\) from both sides: \(y=180^{\circ}-80^{\circ}\).

Answer:

\(100\)