Question

using algebra find the values of x and y. 20.

Explanation:

Step1: Analyze the triangle with \(x\)

The triangle with \(x\) is an equilateral triangle. In an equilateral triangle, all angles are equal. Since the sum of angles in a triangle is \(180^{\circ}\), we have the equation \(x + x+ x=180^{\circ}\).

$$3x = 180^{\circ}$$

$$x=\frac{180^{\circ}}{3}=60^{\circ}$$

Step2: Analyze the triangle with \(y\)

The triangle with \(y\) is an isosceles triangle. The base angles of an isosceles triangle are equal. Also, we know that the side - length relationships (marked with tick - marks) imply that the triangle with \(y\) has angles \(y^{\circ},y^{\circ},60^{\circ}\). Using the angle - sum property of a triangle (\(y + y+60^{\circ}=180^{\circ}\))

$$2y=180^{\circ}- 60^{\circ}$$

$$2y = 120^{\circ}$$

$$y=\frac{120^{\circ}}{2}=60^{\circ}$$

Answer:

\(x = 60^{\circ}\), \(y = 60^{\circ}\)