Question

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

Explanation:

Step1: Recall linear - pair property

Linear - pair angles are supplementary, so \(m\angle1 + m\angle2=180^{\circ}\).
Given \(m\angle1=(5x + 9)^{\circ}\) and \(m\angle2=(3x + 11)^{\circ}\), we have the equation \((5x + 9)+(3x + 11)=180\).

Step2: Combine like - terms

\[

$$\begin{align*} 5x+3x + 9+11&=180\\ 8x+20&=180 \end{align*}$$

\]

Step3: Solve for \(x\)

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

Step4: Find \(m\angle1\)

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

Step5: Find \(m\angle2\)

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

Answer:

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