Question

find the values of x and y
x =
y =

Explanation:

Step1: Find an interior - angle

The exterior angle of 114° and an interior - angle of the triangle are supplementary. Let the interior - angle adjacent to 114° be \(z\). Then \(z + 114^{\circ}=180^{\circ}\), so \(z = 180^{\circ}-114^{\circ}=66^{\circ}\).

Step2: Use the property of an isosceles triangle

Since the triangle has two equal sides (indicated by the marks), the angles opposite those sides are equal. Let the other two interior angles of the triangle be \(x\) and \(y\), and \(x = y\).

Step3: Apply the angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So \(x + y+z = 180^{\circ}\). Substitute \(z = 66^{\circ}\) and \(y = x\) into the equation: \(x + x+66^{\circ}=180^{\circ}\), which simplifies to \(2x=180^{\circ}-66^{\circ}=114^{\circ}\). Then \(x=\frac{114^{\circ}}{2}=57^{\circ}\), and since \(y = x\), \(y = 57^{\circ}\).

Answer:

\(x = 57\), \(y = 57\)