Question

using algebra find the values of x and y. 22.

Explanation:

Step1: Find the value of \(x\)

Since \(x\) and \(140^{\circ}\) are supplementary angles (they form a linear pair), we use the formula \(x + 140^{\circ}=180^{\circ}\).
Subtracting \(140^{\circ}\) from both sides gives \(x = 180^{\circ}-140^{\circ}=40^{\circ}\).

Step2: Find the value of \(y\)

The two triangles are congruent (marked with equal sides). In a triangle, the sum of angles is \(180^{\circ}\). For the triangle with angle \(x = 40^{\circ}\), we have \(y+40^{\circ}+60^{\circ}=180^{\circ}\).
First, add \(40^{\circ}\) and \(60^{\circ}\): \(40^{\circ}+60^{\circ} = 100^{\circ}\). Then subtract from \(180^{\circ}\): \(y=180^{\circ}-(40^{\circ}+60^{\circ})=80^{\circ}\).

Answer:

\(x = 40\), \(y = 80\)