Question

find the values of x and y

Explanation:

Step1: Find the value of \( y \)

Since the sum of adjacent angles on a straight line is \( 180^{\circ} \), we have \( y + 111=180 \).
Subtracting 111 from both sides gives \( y = 180 - 111=69 \).

Step2: Find the value of \( x \)

The triangle is isosceles (two sides are equal), so the base - angles are equal.
Using the angle - sum property of a triangle (\( x + 2y=180 \)).
Substitute \( y = 69 \) into the equation: \( x+2\times69 = 180 \).
Simplify: \( x+138 = 180 \).
Subtract 138 from both sides: \( x=180 - 138 = 42 \).

Answer:

\( x = 42 \), \( y = 69 \)