In the figure below, lines l_{1} // l_{2}. Lines l_{3}, l_{4} and l_{1} intesect at point O. If the angle 3 = 120^{o}
and angle 1 = 80^{o}, what is the degree measure of angle 2?

Solution:

since l_{3} and l_{4} intersect at point O (Given)

so angle 1 = angle AOB (vertical angles are equal)

since l_{1} // l_{2} (Given)

so angle 3 = angle AOC (alternate interior angles are equal)

angle AOC = angle AOB + angle BOC

angle 3 = angle 1 + angle 2

so angle 2 = angle 3 - angle 1

= 120^{o} - 80^{o}

= 40^{o}

therefore, the degree measure of the angle 2 is 40^{o}