SOLUTION: One angle is 27 less than 2 times another. Find the measure of each angle if: a.They are complements of each other. b.They are supplements of each other.

Algebra ->  Angles -> SOLUTION: One angle is 27 less than 2 times another. Find the measure of each angle if: a.They are complements of each other. b.They are supplements of each other.      Log On


   

Question 1152344: One angle is 27 less than 2 times another. Find the measure of each angle if:
a.They are complements of each other.
b.They are supplements of each other.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
let angles be alpha and beta
if angle alpha is 27 less than 2 times beta, we have
alpha=2beta-27........eq.1

a.They are complements of each other.

complementary angles are two angles whose sum is 90°
=>alpha%2Bbeta=90....substitute alpha from eq.1
2beta-27%2Bbeta=90
3beta=90%2B27
3beta=117
beta=117%2F3
beta=39°

then,
alpha=2beta-27........eq.1
alpha=2%2A39-27
alpha=51°

b.They are supplements of each other.
supplementary angles are two angles whose sum is 180°
=>alpha%2Bbeta=180....substitute alpha from eq.1
2beta-27%2Bbeta=180
3beta=180%2B27
3beta=207
beta=207%2F3
beta=69°
then,
alpha=2beta-27........eq.1
alpha=2%2A69-27
alpha=111°

so,
complementary angles are: +51° and 39°
supplementary angles are: +111° and 69°