Answer:
The angles measure 18° and 72°.
Explanation:
81 and 9 is not correct for this problem.
9 is not 1/4 of 81, so 9 and 81 cannot be the answer, although it is true that angles measuring 9° and 81° are complementary since 9 + 81 = 90.
You need to know what complementary angles are.
Definition:
Two angles are complementary if the sum of their measures is 90°.
Each angle is said to be the complement of the other angle.
You have two complementary angles, both of whose measures are unknown.
Call the smaller measure x and the larger measure y.
Since the angles are complementary, the sum of their measures is 90°.
x + y = 90
The measure of one angle is 1/4 the measure of the other angle.
If the smaller angle's measure is 1/4 of the larger angle's measure, then the larger angle's measure is 4 times the smaller angle's measure.
That means that y = 4x.
You have two equations and two unknowns:
x + y = 90
y = 4x
This is a system of equations. We will solve it using the substitution method.
Since y = 4x, where you see y in the first equation, substitute it with 4x
x + y = 90
x + 4x = 90
5x = 90
Divide both sides by 5.
x = 18 <---- smaller angle
y = 4x = 4(18) = 72 <----- larger angle
Answer: The angles measure 18° and 72°.
Check: Do the measures 18 and 72 add to 90?
18 + 72 = 90 Yes.
Is the measure of the smaller angle 1/4 the measure of the larger angle?
18/72 = 9/36 = 1/4 Yes.
18 and 72 is the correct answer.