Question

1. use the exterior angle theorem to find the value of x.

x =

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, \(9x - 15=(4x + 11)+(2x + 22)\).

Step2: Simplify the right - hand side

Combine like terms on the right - hand side: \((4x+2x)+(11 + 22)=6x+33\). The equation becomes \(9x - 15=6x+33\).

Step3: Solve for \(x\)

Subtract \(6x\) from both sides: \(9x-6x - 15=6x-6x + 33\), which simplifies to \(3x-15 = 33\). Then add \(15\) to both sides: \(3x-15 + 15=33 + 15\), so \(3x=48\). Divide both sides by \(3\): \(x=\frac{48}{3}\).

Answer:

\(x = 16\)