Line r is parallel to line t Find the measurement of Angle 6

Line r is parallel to line t. Find the measurement of Angle 6. The diagram is not to scale.

A. 138

B. 32

C. 142

D. 42

Solution

Given are two parallel lines.

As angles on the same line add up to 180 degrees,
138 + m(3) = 180
m(3) = 180 - 138 = 42

Here angles 3 and 4 are alternate interior angles and are equal.
Therefore, m(3) = m(4) = 42

Angles 4 and 6 are vertically opposite angles, hence, are equal.
m(4) = m(6) = 42

Option D. 42 is the required answer.