if angle A contains 1/2x and angle B contains 1/2(180-x) are the angles A and B supplementary, complementary, or neither
To determine whether angles A and B are supplementary, complementary, or neither, let's first understand the definitions of these terms.
1. Supplementary angles: Two angles are supplementary if the sum of their measures is equal to 180 degrees.
2. Complementary angles: Two angles are complementary if the sum of their measures is equal to 90 degrees.
Now let's solve the problem step by step.
Given:
- Angle A contains 1/2x
- Angle B contains 1/2(180-x)
To find out the relationship between A and B, we need to find the measures of these angles.
1. Angle A contains 1/2x.
2. Angle B contains 1/2(180-x).
To simplify, let's solve 1/2(180-x):
1/2(180-x) = 90 - 1/2x
So, angle B contains 90 - 1/2x.
To determine the relationship between angles A and B, we need to evaluate their sum.
Angle A + Angle B = (1/2x) + (90 - 1/2x)
= 90 degrees.
Now, let's analyze the sum:
Since the sum of Angle A and Angle B is equal to 90 degrees, we can conclude that Angle A and Angle B are complementary.
Therefore, the angles A and B are complementary angles.