Question

m∠xyz = 60°, angle diagram with (3x)° and 27° angles, sections for type of angles, key information, equation, solution

Explanation:

Step1: Identify angle relationship

The angle \( \angle XYZ = 60^\circ \) is composed of \( \angle XYW=(3x)^\circ \) and \( \angle WYZ = 27^\circ \). So, the sum of these two angles equals \( \angle XYZ \).
\[
3x + 27 = 60
\]

Step2: Solve for \( x \)

Subtract 27 from both sides:
\[
3x = 60 - 27
\]
\[
3x = 33
\]
Divide both sides by 3:
\[
x=\frac{33}{3}=11
\]

Answer:

\( x = 11 \)