Question

what is the measure of the exterior angle?

Explanation:

Step1: Recall exterior - angle theorem

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(8x + 12=(4x - 4)+60\).

Step2: Solve the equation for \(x\)

First, simplify the right - hand side: \(8x + 12=4x+56\). Then subtract \(4x\) from both sides: \(8x-4x + 12=4x-4x + 56\), which gives \(4x+12 = 56\). Next, subtract 12 from both sides: \(4x+12 - 12=56 - 12\), so \(4x=44\). Divide both sides by 4: \(x = 11\).

Step3: Find the measure of the exterior angle

Substitute \(x = 11\) into the expression for the exterior angle \(8x + 12\). So, \(8\times11+12=88 + 12=100\).

Answer:

\(100^{\circ}\)