SOLUTION: Angle A and angle B are complementary. The measure of angle B is 3 times the measure of A. Find the measure of angles A and B.

Algebra ->  Algebra  -> Angles -> SOLUTION: Angle A and angle B are complementary. The measure of angle B is 3 times the measure of A. Find the measure of angles A and B.      Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 222576: Angle A and angle B are complementary. The measure of angle B is 3 times the measure of A. Find the measure of angles A and B.
Found 3 solutions by rfer, drj, checkley77:
Answer by rfer(10417) About Me  (Show Source):
You can put this solution on YOUR website!
x+3x=90
4x=90
x=22.5degrees
3x=67.5degrees

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Angle A and angle B are complementary. The measure of angle B is 3 times the measure of A. Find the measure of angles A and B.

Step 1. Complementary angles means two angles add up to 90 degrees.

Step 2. Let A be one angle.

Step 3. Let B=90-A be its complement.

Step 4. B=3A or 90-A=3A since the measure of B is 3 time the measure of A.

Step 5. Solving yields the following steps

90-A=3A

Add A to both sides of the equation

90-A%2BA=3A%2BA

90=4A

Divide 4 to both sides of the equation

90%2F4=4A%2F4

22.5=A Then B=3A=67.5

Step 6. ANSWER: The complementary angles are A=22.5 and B=67.5 degrees.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Answer by checkley77(12569) About Me  (Show Source):
You can put this solution on YOUR website!
a+b=90
b=3a
a+(3a)=90
4a=90
a=90/4
a=22.5 degrees for the smaller angle.
22.5+b=90
b=90-22.5
b=67.5 degrees for the larger angle.