Question

if the measure of angle 1 is 118 degrees, what is the measure of angle 8?

Explanation:

Step1: Find the measure of angle 4

Angle 1 and angle 4 are supplementary angles (they form a linear pair).
The sum of supplementary angles is \(180^{\circ}\).
So, \(m\angle4 = 180^{\circ}-m\angle1\)
Substitute \(m\angle1 = 118^{\circ}\) into the formula:
\(m\angle4=180^{\circ}- 118^{\circ}=62^{\circ}\)

Step2: Use the property of corresponding angles

Angle 4 and angle 8 are corresponding angles.
When two parallel lines \(m\) and \(n\) are cut by a transversal \(p\), corresponding angles are equal.
So, \(m\angle8=m\angle4\)

Answer:

\(62^{\circ}\)