Question

∠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

The sum of angles in a linear pair is 180°. So, \(m\angle1 + m\angle2=180^{\circ}\).
Substitute \(m\angle1=(5x + 9)^{\circ}\) and \(m\angle2=(3x + 11)^{\circ}\) into the equation: \((5x + 9)+(3x + 11)=180\).

Step2: Simplify the left - hand side

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

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

Step5: Find \(m\angle2\)

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

Answer:

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