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:
[tex]\frac{1}{3}y = 2x-5[/tex]
According to the given definition we have:
[tex]x + y = 90[/tex]
So, we have two equations with two unknowns:
[tex]\frac{1}{3}y = 2x-5[/tex] -----> (1)
[tex]x + y = 90[/tex] -----> (2)
From (1) we clear y:
[tex]y = 3 * (2x-5)\\y = 6x-15[/tex]
We substitute and in (2):
[tex]x + (6x-15) = 90\\x + 6x-15 = 90\\x + 6x = 90 + 15\\7x = 105[/tex]
[tex]x =\frac{105}{7}\\x = 15[/tex]
Thus, the angle is[tex]x = 15[/tex] degrees.
Answer:
[tex]x = 15 degrees.[/tex]
