Question

In the diagram below, lines a and b are parallel and cut by transversal, t. If angle 1 is 120 degrees, find the measure of angle 660°90°120°180°

Answer 1

Notice that angles 6 and 2 are corresponding angles. Then, their measures are the same.

On the other hand, angles 1 and 2 are supplementary angles, then the sum of their measures is 180º.

Use this fact to find the measure of the angle 2, which is the same as the measure of angle 6.

Since the angles 1 and 2 are supplementary, then:

`m\angle2+m\angle1=180º`

Since the measure of the angle 1 is 120º, then:

`m\angle2+120º=180º`

Solve for the measure of the angle 2:

`\begin{gathered} \Rightarrow m\angle2=180º-120º \\ \Rightarrow m\angle2=60º \end{gathered}`

Since the angles 6 and 2 are corresponding angles, then:

`\begin{gathered} m\angle6=m\angle2 \\ \Rightarrow m\angle6=60º \end{gathered}`

Therefore, the measure of angle 6 is 60º.