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:

$\frac{1}{3}y = 2x-5$

According to the given definition we have:

$x + y = 90$

So, we have two equations with two unknowns:

$\frac{1}{3}y = 2x-5$ -----> (1)

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

From (1) we clear y:

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

We substitute and in (2):

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

$x =\frac{105}{7}\\x = 15$

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

Answer:

$x = 15 degrees.$