Question

Lines l and m are parallel. When they are cut by the two transversals below, a triangle is formed.

What is m < 2?

34 degrees
40 degrees
74 degrees
146 degrees

Answer 1

The measure of angle 1 is 180-74 which is 106. And you have a vertical angle with 40 degrees as the unmarked angle inside your triangle, so that unmarked angle is 40. That means that angle 2 is equal to 180 - 106 - 40 which is 34

Answer 2

The angle marked as 2 in the figure is 34 degrees.

Explanation:

The sum of interior angles of a triangle is 180 degrees.

To know the value of angle 2, you have to solve following equation:

`180=angle1+angle2+angle3`

`angle2=180-angle1-angle3`

`angle2=180-106-40\\angle2=34`

The values of angle 1 and angle 3 are calculated as follows:

• Angle 1

Angle 1 is calculated by doing:

180-74=106

• Angle 3

As angle 3 is opposite to the 40 degrees angle drawn in the figure, and knowing they are vertical angles, you can assume that angle 3 is equal to 40 degrees.