An angle measures 53°. What are the measures of the angle’s complement and supplement? A. complement, 37°; supplement, 137° B. complement, 127°; supplement, 47° C. complement, 37°; supplement, 127° D. complement, 127°; supplement, 37°
The Correct Answer and Explanation is:
To find the complement and supplement of a given angle, you use two basic 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.
In this case, the given angle is 53°.
Step 1: Find the complement
To find the complement, subtract the given angle from 90°:90°−53°=37°90° – 53° = 37°90°−53°=37°
So, the complement of 53° is 37°.
Step 2: Find the supplement
To find the supplement, subtract the given angle from 180°:180°−53°=127°180° – 53° = 127°180°−53°=127°
So, the supplement of 53° is 127°.
Final Answer:
- Complement: 37°
- Supplement: 127°
Correct Choice:
C. complement, 37°; supplement, 127°
Explanation:
The concept of complementary and supplementary angles is foundational in geometry. Complementary angles often appear when working with right triangles or perpendicular lines. Supplementary angles frequently arise when dealing with straight lines or adjacent angles on a straight angle.
Knowing how to find complements and supplements helps in solving problems involving unknown angles, parallel lines cut by a transversal, and properties of polygons. For any angle less than 90°, you can always find a complement. For any angle less than 180°, you can always find a supplement. Since 53° is less than both 90° and 180°, both complement and supplement exist in this case.
This understanding supports problem-solving in geometry, trigonometry, and even in real-life applications like design and construction where precise angle measurements are crucial.
