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

Answer:

$\boxed{\theta=35^{\circ}}$

Step-by-step 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 $\beta=55^{\circ}$