(a) An angle measures 54°. What is the measure of its supplement? (b) An angle measures 49°. What is the measure of its complement? measure of the supplement: measure of the complement:
The Correct Answer and Explanation is:
To solve these problems, we must understand the definitions of complementary and supplementary angles:
- Complementary angles are two angles whose measures add up to 90 degrees.
- Supplementary angles are two angles whose measures add up to 180 degrees.
(a) An angle measures 54°. What is the measure of its supplement?
To find the supplement: 180°−54°=126°180° – 54° = 126°180°−54°=126°
So, the measure of the supplement is 126 degrees.
(b) An angle measures 49°. What is the measure of its complement?
To find the complement: 90°−49°=41°90° – 49° = 41°90°−49°=41°
So, the measure of the complement is 41 degrees.
Final Answers:
- Measure of the supplement of 54°: 126 degrees
- Measure of the complement of 49°: 41 degrees
Explanation:
Angles are measured in degrees, and certain pairs of angles have special relationships. Complementary angles form a right angle when added together, meaning their total is always 90 degrees. If one angle is known, subtracting it from 90 degrees gives the missing complementary angle.
For example, if you know one angle is 49 degrees, its complement must be: 90°−49°=41°90° – 49° = 41°90°−49°=41°
So, 49 degrees and 41 degrees are complementary.
On the other hand, supplementary angles form a straight line when combined, meaning they total 180 degrees. If one angle is 54 degrees, the other must be: 180°−54°=126°180° – 54° = 126°180°−54°=126°
Therefore, 54 degrees and 126 degrees are supplementary.
These basic definitions and calculations are essential in geometry, especially when dealing with parallel lines, transversals, triangles, and polygons. Understanding them helps with more complex angle relationships and solving geometric proofs or equations.
