143k views
1 vote
One-third of the complement of an angle is five less than two times the angle. Find the angle .

User IlyaGulya
by
6.6k points

1 Answer

0 votes

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.