Question

what are the values of x and y?

x =

y =

Explanation:

Step1: Use the property of isosceles triangle

Since the two sides of the triangle are equal (marked with the same tick), the triangle is isosceles. In an isosceles triangle, the base - angles are equal. Let the two base - angles be \(x\) and the third angle is \(40^{\circ}\).
We know that the sum of angles in a triangle is \(180^{\circ}\), so \(x + x+40^{\circ}=180^{\circ}\).
Simplify the equation: \(2x=180^{\circ}- 40^{\circ}=140^{\circ}\), then \(x = 70^{\circ}\).

Step2: Use the property of linear pair

\(y\) and the non - \(x\) angle of the triangle form a linear pair. Since the non - \(x\) angle of the triangle is \(40^{\circ}\) (given) and \(y\) is adjacent to it (forming a straight line, so \(y + 70^{\circ}=180^{\circ}\) (because the non - \(x\) angle of the triangle is \(40^{\circ}\) and we found \(x = 70^{\circ}\) from the triangle angle sum, and \(y\) is supplementary to the angle adjacent to it in the triangle).
So \(y=110^{\circ}\).

Answer:

\(x = 70^{\circ}\), \(y = 110^{\circ}\)