Question 3

60 degrees and 120 degrees are supplementary angles.

Supplementary angles are defined as two angles whose measures add up to 180 degrees. In this case, the pair of angles 60 degrees and 120 degrees sum to 180 degrees, which confirms that they are indeed supplementary.

A) 45 degrees and 45 degrees

This pair adds up to 90 degrees (45 + 45), which does not satisfy the definition of supplementary angles. Therefore, these angles are not supplementary.

B) 72 degrees and 100 degrees

The sum of 72 degrees and 100 degrees is 172 degrees (72 + 100), which also does not equal 180 degrees. Hence, this pair is not supplementary.

C) 35 degrees and 55 degrees

The total for this pair is 90 degrees (35 + 55), failing to reach the 180 degrees required for supplementary angles. Thus, this option is incorrect.

D) 60 degrees and 120 degrees

This pair of angles sums to 180 degrees (60 + 120), confirming that they meet the criteria for supplementary angles. Therefore, this option is correct.

Conclusion

The only pair of angles that qualifies as supplementary in this question is 60 degrees and 120 degrees. The other options do not add up to 180 degrees and thus fail to meet the definition of supplementary angles. This reinforces the understanding of how angle pairs are classified based on their sums.