Question

One-third of the complement of an angle is five less than two times the angle. Find the angle .

Answer 1

For this case we have that by definition:

Complementary angles are those that add up to 90 degrees.

We have the following variables:

x: Angle

y: Complement of the angle

According to the statement we have:

`(1)/(3)y = 2x-5`

According to the given definition we have:

`x + y = 90`

So, we have two equations with two unknowns:

`(1)/(3)y = 2x-5` -----> (1)

`x + y = 90` -----> (2)

From (1) we clear y:

`y = 3 * (2x-5)\\y = 6x-15`

We substitute and in (2):

`x + (6x-15) = 90\\x + 6x-15 = 90\\x + 6x = 90 + 15\\7x = 105`

`x =(105)/(7)\\x = 15`

Thus, the angle is
`x = 15` degrees.

Answer:

`x = 15 degrees.`