Question

In a pair of complementary angles, the measurement of the larger angle is three times that of the smaller angle. Find the measurements of the two angles.

Answer 1

So the meaning of two angles being complimentary simply means that the two angles add up to 90 degrees. Lets call the two angles x and y where x is the smaller angle.
x + y = 90
We also know that y, being the larger angle is 3 times x.
y = 3*x
Given these two we can solve the problem with basic algebra!
x + y =90
x + (3*x) = 90
4*x = 90
x = 90/4
x = 22.5
y = 3 * x
y = 3*(22.5)
y = 67.5

Answer 2

Answer:

Angle L*; 67.5 degrees

Angle S*; 22.5 degrees

Step-by-step explanation:

Angle L is 3 times bigger than Angle S.

With this information, we can make an equation.

L=3S

Complementary angles add up to 90 degrees.

90 = 3S + S

90 = 4S

22.5

Angle S equals 22.5.

Because Angle L is 3 times bigger than Angle S, we multiply 22.5 by 3.

This gives us 67.5.

Angle L is 67.5 degrees

Angle S is 22.5 degrees

Now, in order to check our work, we add the two angles together.

67.5 + 22.5 = 90

Because they add up to 90 degrees, the complementary angles work with each other meaning that we are correct

*Angle L is the larger angle

**Angle S is the smaller angle