Question

The complement of an angle is 10 less than 4 times the angle itself. What is the measure of the angle and its complement?

Answer 1

Below.

Step-by-step explanation:

If the angle is x degrees then its complement is 90-x degrees.

So 90-x = 4x - 10

90 + 10 = 4x + x

5x = 100

x = 20.

and the complement is 90-20 = 70.

Answer 2

The measure of the angle is 20 degrees and its complement is 70 degrees. They are calculated by setting up and solving the equation 90 - x = 4x - 10, reflecting the relationship between the angle and its complement.

Step-by-step explanation:

The subject of this question is Mathematics and it involves the concept of complementary angles. In geometry, two angles are called complementary if their measures add up to 90 degrees. If we let x represent the measure of the angle, then its complement can be represented as 90 - x. According to the question, 90 - x = 4x - 10. Solving this equation for x, we get:

1. Add x to both sides: 90 = 5x - 10
2. Add 10 to both sides: 100 = 5x
3. Divide both sides by 5: x = 20

Therefore, the angle is

20 degrees

and its complement is

70 degrees

. It's important to always check your answer, too. If you add them together, you should get 90 degrees, which is the definition of complementary angles.

Learn more about complementary angles