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

A linear pair of angles sums to \(180^\circ\). 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 and solve for \(x\)

Combine like terms: \(5x+3x + 9 + 11 = 180\)
\(8x+20 = 180\)
Subtract 20 from both sides: \(8x=180 - 20=160\)
Divide by 8: \(x=\frac{160}{8}=20\)

Step3: Find \(m\angle1\)

Substitute \(x = 20\) into \(m\angle1=(5x + 9)^\circ\):
\(m\angle1=5(20)+9=100 + 9 = 109^\circ\)

Step4: Find \(m\angle2\)

Substitute \(x = 20\) into \(m\angle2=(3x + 11)^\circ\):
\(m\angle2=3(20)+11=60 + 11 = 71^\circ\)

Answer:

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