Question

what are the values of x and y?

Explanation:

Step1: Identify the triangle type

Since two sides of the triangle are equal (marked with red ticks), it is an isosceles triangle. In an isosceles triangle, the base - angles are equal. So, \(y = 72^{\circ}\).

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). Let \(x\) be the third angle. Then \(x + y+72^{\circ}=180^{\circ}\). Substitute \(y = 72^{\circ}\) into the equation: \(x+72^{\circ}+72^{\circ}=180^{\circ}\).

$$x=180^{\circ}-(72^{\circ}+72^{\circ})$$

$$x = 180^{\circ}-144^{\circ}$$

$$x = 36^{\circ}$$

Answer:

\(x = 36\), \(y = 72\)