SOLUTION: An angle measures 6° less than the measure of its complementary angle. What is the measure of each angle?

Algebra ->  Angles -> SOLUTION: An angle measures 6° less than the measure of its complementary angle. What is the measure of each angle?      Log On


   

Question 1198663: An angle measures 6° less than the measure of its complementary angle. What is the measure of each angle?
Found 3 solutions by josgarithmetic, MathLover1, math_tutor2020:
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
m, the measure of this angle

m=-6%2B%2890-m%29-----------the description.
Solve.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

complementary angles are two angles whose sum is 90°
let one angle be alpha and the other beta
alpha+%2B+beta=90

if an angle measures 6° less than the measure of its complementary angle
alpha=beta-6
substitute in
alpha+%2B+beta=90
beta-6+%2B+beta=90
2beta=90%2B6
2beta=96
beta=48

then
alpha=48-6
alpha=42

one angle measures 42° and the measure of its complementary angle is 48


Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

x = some unknown angle
90-x = the complementary angle of x
Take notice how the two angles add to 90.

If the angle x is 6 degrees less than the complement 90-x, then,
x = (90-x) - 6
x = 90-6-x
x = 84-x
x+x = 84
2x = 84
x = 84/2
x = 42
90-x = 90-42 = 48

We can see that the angle 42 degrees is indeed 6 degrees smaller than its complement 48 degrees (48-6 = 42)
As a check:
42+48 = 90
showing they are complementary angles

Answers: 42 degrees and 48 degrees