Question

the measure of the exterior angle of the triangle is square^{circ}.

Explanation:

Step1: Apply the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.
So, \(3x + 6=(2x + 18)+24\).

Step2: Solve the equation for \(x\)

Simplify the right - hand side: \(3x+6 = 2x+42\).
Subtract \(2x\) from both sides: \(3x - 2x+6=2x - 2x + 42\), which gives \(x+6 = 42\).
Subtract \(6\) from both sides: \(x=42 - 6=36\).

Step3: Find the measure of the exterior angle

Substitute \(x = 36\) into the expression for the exterior angle \((3x + 6)\).
\(3x+6=3\times36+6\).
First, calculate \(3\times36 = 108\), then \(108+6=114\).

Answer:

\(114\)