Question

1. ∠1 and ∠2 form a linear pair. if m∠1 = (18x - 1)° and m∠2 = (23x + 17)°, find m∠2.

Explanation:

Step1: Recall linear pair property

A linear pair of angles sums to \(180^\circ\). So, \(m\angle1 + m\angle2 = 180^\circ\).
Substitute \(m\angle1=(18x - 1)^\circ\) and \(m\angle2=(23x + 17)^\circ\):
\((18x - 1)+(23x + 17)=180\)

Step2: Solve for \(x\)

Combine like terms: \(18x + 23x - 1 + 17 = 180\)
\(41x + 16 = 180\)
Subtract 16 from both sides: \(41x = 180 - 16 = 164\)
Divide by 41: \(x=\frac{164}{41}=4\)

Step3: Find \(m\angle2\)

Substitute \(x = 4\) into \(m\angle2=(23x + 17)^\circ\):
\(m\angle2=23(4)+17=92 + 17 = 109^\circ\)

Answer:

\(109^\circ\)