Question

question
find ( mangle srq ).
answer attempt 1 out of 2
( mangle srq=)

Explanation:

Step1: Identify the triangle type

Since two sides of the triangle are marked as equal (by the tick marks), it is an isosceles triangle. In an isosceles triangle, the base - angles are equal.

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). Let \(m\angle SRQ=m\angle SQR = x\) (because of the isosceles triangle property, as the sides opposite these angles are equal). We know one angle \(m\angle SQR = 60^{\circ}\). Using the formula \(m\angle SRQ+m\angle SQR+m\angle QSR=180^{\circ}\). Substituting \(m\angle SQR = 60^{\circ}\) and \(m\angle SRQ=x\), we get \(x + 60^{\circ}+x=180^{\circ}\) (but since \(x = 60^{\circ}\) from the base - angle equality in the isosceles triangle with one angle \(60^{\circ}\), the triangle is equilateral). Another way: If a triangle is isosceles and has an angle of \(60^{\circ}\), then all angles are \(60^{\circ}\).

Answer:

\(60\)