Question

question 10
2 pts
what is the value of the exterior angle?
(enter your answer as a number only)

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, \(7x - 16=(x + 8)+4x\).

Step2: Simplify the equation

Simplify the right - hand side: \((x + 8)+4x=5x + 8\). The equation becomes \(7x-16 = 5x+8\).

Step3: Solve for \(x\)

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

Step4: Find the value of the exterior angle

Substitute \(x = 12\) into \(7x-16\). \(7\times12-16=84 - 16=68\).

Answer:

68