Question

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

Explanation:

Step1: Apply exterior angle theorem

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, we have the equation:
$$3x + 6=24+(2x + 18)$$

Step2: Simplify the right - hand side

Simplify the right - hand side of the equation: \(24+(2x + 18)=2x+24 + 18=2x + 42\)
So the equation becomes \(3x+6 = 2x + 42\)

Step3: Solve for x

Subtract \(2x\) from both sides: \(3x-2x+6=2x - 2x+42\), which simplifies to \(x + 6=42\)
Then subtract 6 from both sides: \(x=42 - 6=36\)

Step4: Find the measure of the exterior angle

Substitute \(x = 36\) into the expression for the exterior angle \((3x + 6)^{\circ}\)
\(3x+6=3\times36+6=108 + 6=114\)

Answer:

\(114\)