Problem:

Find an angle if 7 times its complement is 10 less than 3 times its supplement.

Solution:

Let's assume the angle as x.

Complement:
The complement of an angle is the angle that, when added to the given angle, equals 90 degrees. The complement of x is denoted as (90 - x).

Supplement:
The supplement of an angle is the angle that, when added to the given angle, equals 180 degrees. The supplement of x is denoted as (180 - x).

Given:
7 times the complement of x is 10 less than 3 times the supplement of x.

7(90 - x) = 3(180 - x) - 10

Simplifying:
630 - 7x = 540 - 3x - 10

Combining like terms:
630 - 7x = 530 - 3x

Moving variables to one side:
630 - 530 = 3x - 7x

100 = -4x

Dividing by -4:
x = -25

Therefore, the angle is -25 degrees.

Explanation:

To solve the problem, we need to set up an equation based on the given information. We assume the angle as x and express the complement and supplement in terms of x.

We are given that 7 times the complement of x is 10 less than 3 times the supplement of x. We can write this as an equation: 7(90 - x) = 3(180 - x) - 10.

By simplifying and combining like terms, we can solve for x. Moving the variables to one side, we get 630 - 7x = 530 - 3x. Simplifying further, we have 100 = -4x.

Dividing both sides by -4, we find that x = -25.

Therefore, the angle is -25 degrees.