Question

in the figure below, ( mangle1 = 3x^{circ} ) and ( mangle2=(x + 36)^{circ} ). find the angle measures.

Explanation:

Step1: Use the property of supplementary angles

Supplementary angles sum to \(180^{\circ}\). So, \(m\angle1 + m\angle2=180^{\circ}\).
Substitute \(m\angle1 = 3x^{\circ}\) and \(m\angle2=(x + 36)^{\circ}\) into the equation:
\(3x+(x + 36)=180\).

Step2: Solve the equation for \(x\)

Combine like - terms: \(3x+x+36 = 180\), which simplifies to \(4x+36=180\).
Subtract 36 from both sides: \(4x=180 - 36\), so \(4x=144\).
Divide both sides by 4: \(x=\frac{144}{4}=36\).

Step3: Find \(m\angle1\)

Substitute \(x = 36\) into \(m\angle1 = 3x^{\circ}\). Then \(m\angle1=3\times36^{\circ}=108^{\circ}\).

Step4: Find \(m\angle2\)

Substitute \(x = 36\) into \(m\angle2=(x + 36)^{\circ}\). Then \(m\angle2=(36 + 36)^{\circ}=72^{\circ}\).

Answer:

\(m\angle1 = 108^{\circ}\)
\(m\angle2 = 72^{\circ}\)