Question

in the figure below, ( m angle 1=(x - 24)^{circ} ) and ( m angle 2 = 5x^{circ} ). find the angle measures.

Explanation:

Step1: Use the property of supplementary angles

Since \(\angle1\) and \(\angle2\) are supplementary, \(m\angle1 + m\angle2=180^{\circ}\).
Substitute \(m\angle1=(x - 24)^{\circ}\) and \(m\angle2 = 5x^{\circ}\) into the equation:
\((x-24)+5x=180\)

Step2: Solve the equation for \(x\)

Combine like - terms: \(x+5x-24 = 180\), so \(6x-24=180\).
Add 24 to both sides: \(6x=180 + 24\), \(6x=204\).
Divide both sides by 6: \(x=\frac{204}{6}=34\).

Step3: Find \(m\angle1\)

Substitute \(x = 34\) into \(m\angle1=(x - 24)^{\circ}\):
\(m\angle1=(34-24)^{\circ}=10^{\circ}\).

Step4: Find \(m\angle2\)

Substitute \(x = 34\) into \(m\angle2 = 5x^{\circ}\):
\(m\angle2=5\times34^{\circ}=170^{\circ}\).

Answer:

\(m\angle1 = 10^{\circ}\), \(m\angle2=170^{\circ}\)