Question

find the values of x and y. 123° x = y =

Explanation:

Step1: Find the value of y

Since the exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. The exterior angle is 123°. The two non - adjacent interior angles are equal (because the triangle has two equal sides as indicated by the marks). Let the non - adjacent interior angles be \(y\). So \(y = 180^{\circ}-123^{\circ}=57^{\circ}\).

Step2: Find the value of x

The sum of the interior angles of a triangle is 180°. Since the two base angles are \(y = 57^{\circ}\) each, then \(x=180^{\circ}-2y\). Substitute \(y = 57^{\circ}\) into the formula: \(x = 180^{\circ}-2\times57^{\circ}=180^{\circ}-114^{\circ}=66^{\circ}\).

Answer:

\(x = 66\)
\(y = 57\)