SOLUTION: One angle of a triangle is 35 degrees greater than the smallest angle and the third angle is 15 degrees less than twice the smallest angle.Find the measures of the 3 angles.

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Question 228468: One angle of a triangle is 35 degrees greater than the smallest angle and the third angle is 15 degrees less than twice the smallest angle.Find the measures of the 3 angles.
Found 2 solutions by drj, rfer:
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
One angle of a triangle is 35 degrees greater than the smallest angle and the third angle is 15 degrees less than twice the smallest angle. Find the measures of the 3 angles.

Step 1. The sum of the three angles for a triangle is 180 degrees.

Step 2. Let x be the smallest angle.

Step 3. Let x+35 be the second angle since it's 35 degrees greater than the smallest angle.

Step 4. Let 2x-15 be the third angle since it is 15 degrees less than twice the first.

Step 5. Then, x%2Bx%2B35%2B2x-15=180 since the sum of the angles is 180 degrees.

Step 6. Solving the equation x%2Bx%2B35%2B2x-15=180 yields the following steps

4x%2B20=180

Subtract 20 from both sides of the equation

4x%2B5-5=180-20

4x=160

x=40 x%2B35=75 and 2x-15=65. Note these three angles add up to 180 degrees as a check.

Step 6. ANSWER: The angles of the triangle are 40, 75, and 65 degrees.

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J

Answer by rfer(16322) About Me  (Show Source):
You can put this solution on YOUR website!
x+x+35+2x-15=180
4x+20=180
4x=160
x=40
x+35=75
2x-15=65