Question

18
the measure of the exterior angle of the triangle is
(x + 8)°
(7x - 16)°
4x°

Explanation:

Step1: Use 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, we have the equation \(7x - 16=(x + 8)+4x\).

Step2: Simplify the right - hand side of the equation

Simplify \((x + 8)+4x\) to get \(x+4x + 8=5x + 8\). So the equation becomes \(7x-16 = 5x+8\).

Step3: Solve for \(x\)

Subtract \(5x\) from both sides: \(7x-5x-16=5x - 5x+8\), which simplifies to \(2x-16 = 8\). Then add \(16\) to both sides: \(2x-16 + 16=8 + 16\), so \(2x=24\). Divide both sides by \(2\): \(x=\frac{24}{2}=12\).

Step4: Find the measure of the exterior angle

Substitute \(x = 12\) into the expression for the exterior angle \(7x-16\). We get \(7\times12-16=84 - 16=68\).

Answer:

\(68\)