Question

1. find ( mangle wvz ) if ( mangle wvz=(x - 5)^{circ},mangle zvu=(2x + 7)^{circ} ), and ( mangle wvu = 110^{circ} ).

Explanation:

Step1: Use angle - addition postulate

By the angle - addition postulate, \(m\angle WVZ+m\angle ZVU = m\angle WVU\).
Substitute the given angle measures: \((x - 5)+(2x + 7)=110\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(x-5 + 2x+7=(x + 2x)+(-5 + 7)=3x+2\).
So the equation becomes \(3x+2 = 110\).

Step3: Solve for \(x\)

Subtract 2 from both sides: \(3x+2-2=110 - 2\), which gives \(3x=108\).
Divide both sides by 3: \(x=\frac{108}{3}=36\).

Step4: Find \(m\angle WVZ\)

Substitute \(x = 36\) into the formula for \(m\angle WVZ\).
\(m\angle WVZ=(x - 5)^{\circ}\), so \(m\angle WVZ=(36-5)^{\circ}=31^{\circ}\).

Answer:

\(31^{\circ}\)