Question

Suppose that an angle's supplement is 155°. Find the measure of its complement.
Responses
A 55°
B 65°
C 75°
D 85°

Answer 1

please explain

Answer 2

B 65°

Explanation:
The sum of an angle and its complement is 90°.
The sum of an angle and its supplement is 180°.
Therefore, if the supplement of an angle is 155°, then the angle itself would be 180° - 155° = 25°.
The complement of an angle of 25° would be 90° - 25° = 65°.

Answer 3

Certainly! Here's a more detailed explanation:

1. The definition of a complement: The complement of an angle is the angle that when added to the original angle, gives 90°. For example, if an angle is x degrees, then its complement is 90° - x degrees.

2. The definition of a supplement: The supplement of an angle is the angle that when added to the original angle, gives 180°. For example, if an angle is x degrees, then its supplement is 180° - x degrees.

3. Given information: In this case, the angle's supplement is 155°. This means that when you add this angle to the original angle, you will get 180°. So, let's call the original angle "x" degrees.

4. Relationship between original angle, supplement, and complement: Since the supplement of an angle is 180° - x (original angle), and the complement of an angle is 90° - x, we can set up the relationship like this:

Original angle (x) + Supplement (155°) = 180°
x + 155 = 180

Original angle (x) + Complement (90°) = 90°
x + 90 = 90

5. Solving for x: If you solve the first equation above, you will get:

x + 155 = 180
x = 180 - 155
x = 25

So, the original angle is 25°.

6. Finding the complement: To find the complement of the original angle, you subtract the original angle (25°) from 90°:

Complement = 90° - x
Complement = 90° - 25°
Complement = 65°

Therefore, the complement of an angle whose supplement is 155° is 65°.