Question

in the figure below, ( mangle1=(x + 36)^{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 \(m\angle1=(x + 36)^{\circ}\) and \(m\angle2 = 2x^{\circ}\) into the equation: \((x + 36)+2x=90\).

Step2: Simplify the equation

Combine like - terms: \(3x+36 = 90\).
Subtract 36 from both sides: \(3x=90 - 36\), so \(3x=54\).

Step3: Solve for \(x\)

Divide both sides by 3: \(x=\frac{54}{3}=18\).

Step4: Find \(m\angle1\)

Substitute \(x = 18\) into \(m\angle1=(x + 36)^{\circ}\): \(m\angle1=(18 + 36)^{\circ}=54^{\circ}\).

Step5: Find \(m\angle2\)

Substitute \(x = 18\) into \(m\angle2=2x^{\circ}\): \(m\angle2=2\times18^{\circ}=36^{\circ}\).

Answer:

\(m\angle1 = 54^{\circ}\), \(m\angle2=36^{\circ}\)