Question

using algebra find the values of x and y. 25.

Explanation:

Step1: Find \(x\)

In an isosceles triangle with a \(60^{\circ}\) angle, it is equilateral. The right - angled triangle has an angle \(x\). Using the property that the sum of angles in a triangle is \(180^{\circ}\), and one angle is \(90^{\circ}\), another is \(60^{\circ}\). So \(x = 30\) (since \(180-(90 + 60)=30\)).

Step2: Find \(y\)

The two triangles are congruent (by properties of the figure, assume side - side - side or other congruence criteria). The angle \(y\) is equal to \(60^{\circ}\) (corresponding angles of congruent triangles).

Answer:

\(x = 30\), \(y=60\)