Question

1. find the value of x.

Explanation:

Step1: Apply the exterior - angle theorem

The exterior - angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles.
So, \((2x + 20)+(5x - 11)=11x - 63\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((2x+5x)+(20 - 11)=11x - 63\), which gives \(7x + 9=11x - 63\).

Step3: Solve for \(x\)

Subtract \(7x\) from both sides: \(7x-7x + 9=11x-7x - 63\), so \(9 = 4x-63\).
Add \(63\) to both sides: \(9 + 63=4x-63 + 63\), which gives \(72 = 4x\).
Divide both sides by \(4\): \(x=\frac{72}{4}\).

Answer:

\(x = 18\)