Question

in the figure below, ( mangle1=(x + 33)^{circ} ) and ( mangle2 = 2x^{circ} ). find the angle measures.

Explanation:

Step1: Use the property of complementary angles

Since \(\angle1\) and \(\angle2\) are complementary, \(m\angle1 + m\angle2=90^{\circ}\). Substitute \(m\angle1=(x + 33)^{\circ}\) and \(m\angle2 = 2x^{\circ}\) into the equation: \((x + 33)+2x=90\).

Step2: Solve the equation for \(x\)

Combine like - terms: \(3x+33 = 90\). Subtract 33 from both sides: \(3x=90 - 33=57\). Divide both sides by 3: \(x=\frac{57}{3}=19\).

Step3: Find \(m\angle1\) and \(m\angle2\)

For \(m\angle1\): Substitute \(x = 19\) into \(m\angle1=(x + 33)^{\circ}\), \(m\angle1=(19 + 33)^{\circ}=52^{\circ}\).
For \(m\angle2\): Substitute \(x = 19\) into \(m\angle2=2x^{\circ}\), \(m\angle2=2\times19^{\circ}=38^{\circ}\).

Answer:

\(m\angle1 = 52^{\circ}\), \(m\angle2 = 38^{\circ}\)