Question

what is the measure of \\( \angle xyz \\)?

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, \(12x - 20=(3x + 11)+(5x + 1)\)

Step2: Simplify the equation

$$
LATEXBLOCK0
$$

Step3: Solve for \(x\)

Subtract \(8x\) from both sides: \(12x-8x-20=8x - 8x+12\), \(4x-20 = 12\)
Add \(20\) to both sides: \(4x-20 + 20=12 + 20\), \(4x=32\)
Divide both sides by \(4\): \(x=\frac{32}{4}=8\)

Step4: Find the measure of \(\angle XYZ\)

\(\angle XYZ = 180-(12x - 20)\) (linear pair)
Substitute \(x = 8\) into the formula:

$$
LATEXBLOCK1
$$

Answer:

\(104^{\circ}\)