An angle measures 48°. What is the measure of its complement? (b) An angle measures 77°. What is the measure of its supplement? measure of the complement: measure of the supplement
The Correct Answer and Explanation is:
Correct Answers
Measure of the complement of 48°: 42°
Measure of the supplement of 77°: 103°
Explanation:
To solve problems involving complementary and supplementary angles, we must first understand their definitions:
- Complementary angles are two angles whose measures add up to 90 degrees.
- Supplementary angles are two angles whose measures add up to 180 degrees.
Part (a): What is the complement of 48°?
We subtract the given angle from 90°:
90° − 48° = 42°
So, the complement of a 48° angle is 42° because 48° + 42° = 90°.
Part (b): What is the supplement of 77°?
We subtract the given angle from 180°:
180° − 77° = 103°
So, the supplement of a 77° angle is 103° because 77° + 103° = 180°.
These kinds of problems often come up in geometry, especially when analyzing shapes like triangles and parallel lines with transversals. In practical terms, knowing complementary and supplementary angles helps in design, construction, engineering, and even animation where precise angle measures are crucial.
It’s also important to note that angles greater than 90° cannot have a complement because the sum would exceed 90°. Similarly, angles greater than or equal to 180° cannot have a supplement for the same reason.
To check your work:
- For complementary angles: the sum must be exactly 90°
- For supplementary angles: the sum must be exactly 180°
Thus:
- 48° + 42° = 90° ✅
- 77° + 103° = 180° ✅
These answers are correct.
