Question

in the figure below, ( mangle wxz = 77^{circ} ), and ( mangle 1 ) is ( 27^{circ} ) more than ( mangle 2 ). find ( mangle 2 ).

Explanation:

Step1: Set up the equation

Let \(m\angle2 = x\). Then \(m\angle1=x + 27^{\circ}\). Since \(m\angle WXZ=m\angle1 + m\angle2\) and \(m\angle WXZ = 77^{\circ}\), we have the equation \(x+(x + 27^{\circ})=77^{\circ}\).

Step2: Simplify the equation

Combine like - terms: \(2x+27^{\circ}=77^{\circ}\).
Subtract \(27^{\circ}\) from both sides: \(2x=77^{\circ}-27^{\circ}\), so \(2x = 50^{\circ}\).

Step3: Solve for \(x\)

Divide both sides by 2: \(x=\frac{50^{\circ}}{2}\).

Answer:

\(25\)