Question

1. find the missing angle.

Explanation:

Step1: Identify the shape

The shape is a trapezoid with \(SR = PQ\) (marked with single - cross), so it is an isosceles trapezoid. In an isosceles trapezoid, base - angles are equal.

Step2: Use angle - sum property of a trapezoid

The sum of the interior angles of a quadrilateral is \(360^{\circ}\). Let the missing angle \(\angle R=x\). Since \(\angle S=\angle P = 60^{\circ}\) (base - angles of isosceles trapezoid), and \(\angle Q=\angle R\) (base - angles of isosceles trapezoid). We have \(x + x+60^{\circ}+60^{\circ}=360^{\circ}\).

Step3: Solve the equation

Combining like terms gives \(2x+120^{\circ}=360^{\circ}\). Subtract \(120^{\circ}\) from both sides: \(2x=360^{\circ}- 120^{\circ}=240^{\circ}\). Divide both sides by 2: \(x = 120^{\circ}\).

Answer:

\(120\)