Question

find the values of x and y.

Explanation:

Step1: Find the adjacent angle of \(119^{\circ}\)

The sum of adjacent angles is \(180^{\circ}\). Let the adjacent angle be \(z\).
\(z = 180 - 119=61^{\circ}\)

Step2: Use the property of isosceles triangle

Since the triangle is isosceles (two sides are equal), the base - angles are equal. So the other base - angle is also \(61^{\circ}\).
Use the angle - sum property of a triangle (\(x + 61+61 = 180\)).
\(x=180-(61 + 61)=58^{\circ}\)

Step3: Find \(y\)

\(y\) and \(61^{\circ}\) are adjacent angles (\(y + 61=180\)).
\(y = 180 - 61=119^{\circ}\)

Answer:

\(x = 58^{\circ}\), \(y = 119^{\circ}\)