Question

o)
(5x - 8)°
2x°
(112 - x)°

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, \(5x - 8=2x+(112 - x)\)

Step2: Simplify the right - hand side of the equation

Simplify \(2x+(112 - x)\):
\(2x+(112 - x)=2x + 112-x=x + 112\)
The equation becomes \(5x-8=x + 112\)

Step3: Solve for \(x\)

Subtract \(x\) from both sides:
\(5x-x-8=x-x + 112\)
\(4x-8=112\)
Add \(8\) to both sides:
\(4x-8 + 8=112+8\)
\(4x=120\)
Divide both sides by \(4\):
\(x=\frac{120}{4}=30\)

Answer:

\(x = 30\)