SOLUTION: The second angle of a triangle is three times the first and the third is 12 degrees less than twice the first. Find the measures of the angles.

Algebra ->  Angles -> SOLUTION: The second angle of a triangle is three times the first and the third is 12 degrees less than twice the first. Find the measures of the angles.       Log On


   

Question 227900: The second angle of a triangle is three times the first and the third is 12 degrees less than twice the first. Find the measures of the angles.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The second angle of a triangle is three times the first and the third is 12 degrees less than twice the first. Find the measures of the angles.

Step 1. Let x be the first angle.

Step 2. Let 3x be the second angle since it's three times the first.

Step 3. Let 2x-12 be the third angle since it's 12 degrees less than twice the first.

Step 4. We note that the sum of the three angles of a triangle is equal to 180 degrees. Then, x+3x+2x-12=180 or 6x=180+12=192.

Step 5. Solving yields the following steps.

6x=192

Divide by 6 to both sides of the equation

6x%2F6=192%2F6

x=32 3x=96 and 2x-12=64-12=52

Check if angles equal to 180 degrees: 32%2B96%2B52=180 which it does.

Step 6. ANSWER: The first angle is 32 degrees, the second angle is 96 degrees, and the third angle is 52 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.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV