Question

in the figure below, m∠wxz = 117°, and m∠1 is 55° more than m∠2. find m∠2.

Explanation:

Step1: Set up the relationship between angles

Let \(m\angle2 = x\). Then \(m\angle1=x + 55^{\circ}\).

Step2: Use the angle - sum property

Since \(m\angle WXZ=m\angle1 + m\angle2\) and \(m\angle WXZ = 117^{\circ}\), we have the equation \((x + 55^{\circ})+x=117^{\circ}\).

Step3: Simplify the equation

Combining like - terms, we get \(2x+55^{\circ}=117^{\circ}\).

Step4: Solve for \(x\)

Subtract \(55^{\circ}\) from both sides: \(2x=117^{\circ}-55^{\circ}=62^{\circ}\). Then divide both sides by 2: \(x = 31^{\circ}\).

Answer:

\(31\)