Question

find the values of x and y.
x=

y=

Explanation:

Step1: Find the value of \( y \)

Use the property that the sum of adjacent angles on a straight line is \( 180^{\circ} \).
\( y + 119^{\circ}=180^{\circ} \)
\( y = 180^{\circ}-119^{\circ}=61^{\circ} \)

Step2: Find the value of \( x \)

Since the triangle has two equal - length sides (marked with the same tick - marks), it is an isosceles triangle. In an isosceles triangle, the base angles are equal.
The sum of angles in a triangle is \( 180^{\circ} \). Let the base angles be \( y\) and \( x\).
\( x + y+40^{\circ}=180^{\circ} \)
Substitute \( y = 61^{\circ} \) into the equation:
\( x+61^{\circ}+40^{\circ}=180^{\circ} \)
\( x=180^{\circ}-(61^{\circ} + 40^{\circ})=79^{\circ} \)

Answer:

\( x = 79\), \( y = 61\)