Question

an isosceles triangle containing two angles with equal measure is shown. the degree measure of each triangles three interior angles and an extra angle is represented with variables. find the measure of the three interior angles. what is the measure of angle x? x = square^{circ} what is the measure of angle y? y = square^{circ}

Explanation:

Step1: Use the exterior - angle property

The exterior - angle property of a triangle states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(y + y=2x - 15\), which simplifies to \(2y=2x - 15\) or \(y=x-\frac{15}{2}\).

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(x + y + y=180\). Substitute \(y=x - 7.5\) into \(x + 2y=180\). We get \(x+2(x - 7.5)=180\).
Expand the left - hand side: \(x + 2x-15 = 180\).
Combine like terms: \(3x=180 + 15\).
So, \(3x=195\).
Solve for \(x\): \(x = 65\).

Step3: Find the value of \(y\)

Substitute \(x = 65\) into \(y=x - 7.5\). Then \(y=65-7.5=57.5\).

Answer:

The measure of angle \(x\) is \(65^{\circ}\) and the measure of angle \(y\) is \(57.5^{\circ}\).