Supplementary angles are pairs of angles that have a sum of 180 degrees. These angles are often adjacent and form a linear pair, but this is not always necessary.
In this problem, we have 4 pairs of angles to determine if they are supplementary. We can tell which angles are supplementary from the diagram.
Vertical angles are always congruent. And with parallel lines, corresponding angles are congruent.
Using this information we can determine that angles 2, 3, 6, and 7 are congruent and that angles 1, 4, 5, and 8 are congruent.
This means that angles 2, 3, 6, and 7 all have an angles measure of 120 degrees as given in the diagram. We can also determine that angles 1, 4, 5, and 8 all have angles measures of 60 degrees.
Since the sum of supplementary angles must be 180 degrees, we can add up the measures of the given pairs of angles to determine if they are supplementary.
A). 1 and 6
The measure of angle 1 is 60 and the measure of angle 6 is 120.
120+60=180
Angles 1 and 6 are supplementary angles.
B). 2 and 3
The measure of angle 2 is 120. The measure of angle 3 is also 120.
120+120=240
Angles 2 and 3 are not supplementary angles.
C). 5 and 8
The measure of angle 5 is 60. The measure of angle 8 is also 60.
60+60=120
Angles 5 and 8 are not supplementary.
D). 5 and 7
The measure of angle 5 is 60. The measure of angle 7 is 120.
120+60=180
Angles 5 and 7 are supplementary.
In this problem, we can determine that the pairs of angles (1 and 6) and (5 and 7) are supplementary angles.
The solution is A and D.
