Question

Lines m and n are parallel. What is the measure of angle 1?

1) 48 degrees

2) 132 degrees

3) 180 degrees

4) 42 degrees

Answer 1

Answer: Choice 1) 48 degrees

The fact that line m is parallel to line n is irrelevant info for this problem. We know that the angle supplementary to angle 1 is the 132 degree angle. This is because these two angles form a straight (180 degree) angle.

So, x+132 = 180 solves to x = 180-132 = 48

Answer 2

The measure of angle 1 is 1) 48 degrees.

Explanation:

The line ''t'' is intercepted by the line ''m'' whose direction is different to the direction of the line ''t''. Wherever this happen, this will create four angles.

In this case, we have the angles 1, 2 , 3 and the 132° angle.

Now, each pair of consecutive angles will be a pair of supplementary angles (angles that add up to 180°).

For example, we know that the angle 1 and the angle 2 add up to 180°.

Applying this fact to the angle 1 and the 132° angle we can write :

`Angle_(1)+132=180`

`Angle_(1)=180-132`

`Angle_(1)=` 48°

We find out that the measure of angle 1 is 48°. We solved this using the fact that the 132° angle and the angle 1 are supplementary angles.