Question

in the figure below, m∠wxz = 100°, and m∠1 is 48° more than m∠2. find m∠2.

Explanation:

Step1: Set up an equation

Let \(m\angle2 = x\). Then \(m\angle1=x + 48^{\circ}\). Since \(m\angle WXZ=m\angle1 + m\angle2\) and \(m\angle WXZ = 100^{\circ}\), we have the equation \((x + 48^{\circ})+x=100^{\circ}\).

Step2: Combine like - terms

Combine the \(x\) terms: \(2x+48^{\circ}=100^{\circ}\).

Step3: Isolate the variable

Subtract \(48^{\circ}\) from both sides: \(2x=100^{\circ}-48^{\circ}\), so \(2x = 52^{\circ}\).

Step4: Solve for \(x\)

Divide both sides by 2: \(x=\frac{52^{\circ}}{2}=26^{\circ}\).

Answer:

\(26\)