Question

1. ∠1 and ∠2 form a linear pair. if ( m∠1=(5x + 9)^{circ} ) and ( m∠2=(3x + 11)^{circ} ), find the measure of each angle.

Explanation:

Step1: Use the property of linear pair

Since ∠1 and ∠2 form a linear pair, \(m\angle1 + m\angle2=180^{\circ}\). Given \(m\angle1=(5x + 9)^{\circ}\) and \(m\angle2=(3x + 11)^{\circ}\), we have the equation \((5x + 9)+(3x + 11)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(5x+3x+9 + 11=180\), which simplifies to \(8x+20 = 180\).

Step3: Solve for \(x\)

Subtract 20 from both sides: \(8x=180 - 20\), so \(8x=160\). Then divide both sides by 8: \(x=\frac{160}{8}=20\).

Step4: Find \(m\angle1\)

Substitute \(x = 20\) into \(m\angle1=(5x + 9)^{\circ}\). \(m\angle1=(5\times20+9)^{\circ}=(100 + 9)^{\circ}=109^{\circ}\).

Step5: Find \(m\angle2\)

Substitute \(x = 20\) into \(m\angle2=(3x + 11)^{\circ}\). \(m\angle2=(3\times20+11)^{\circ}=(60+11)^{\circ}=71^{\circ}\).

Answer:

\(m\angle1 = 109^{\circ}\) and \(m\angle2=71^{\circ}\)