Question

If the measure of an angle is twenty less then the measure of its complement, what is the measure of the angle?

Answer 1

`\boxed{\theta=35^(\circ)}`

Explanation:

Angles that add up to 90° are called complementary angles. In this problem, say, we have an angle
`\theta`. From geometry, we know that angles that add up to 90° are called complementary angles. So the complement of
`\theta` is:

`\beta=90^(\circ)-\theta`

Thus, the measure of an angle that is twenty less than the measure of its complement can be written as:

`\theta=(90-\theta)-20`

By solving this equation:

`\theta+\theta=70 \\ \\ \therefore 2\theta=70 \\ \\ \therefore \boxed{\theta=35^(\circ)}`

The complement is
`\beta=55^(\circ)`