SOLUTION: In Triangle ABC, Angle B is 8 less then one-half of angle A and angle C is 28 larger than angle A. Find the measure of the three angles of the triangle.

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Question 215330: In Triangle ABC, Angle B is 8 less then one-half of angle A and angle C is 28 larger than angle A. Find the measure of the three angles of the triangle.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
In Triangle ABC, Angle B is 8 less then one-half of angle A and angle C is 28 larger than angle A. Find the measure of the three angles of the triangle.

Step 1. The three angles of triangle add up to 180 degrees.

Step 2. Given angle A, then let A%2F2-8 be angle B, and let A%2B28 be angle C

Step 3. Then, add up all the angle to get 180 degrees or A%2BA%2F2-8%2BA%2B8=180. Multiply by 2 to both sides of equation to get rid of denominator.

2%2A%28A%2BA%2F2-8%2BA%2B28%29=2%2A180

2A%2BA-16%2B2A%2B56%29=360

5A=320

A=64

With A=64, then B=A%2F2-8=64%2F2-8=32-8=24 and C=A%2B8=64%2B28=92

Then A+B+C=180 as a check. So 64+24+92=180 or 180=180 which is a true statement.

Step 4. The angles are A=64 degrees, B=24 degrees, and C=92 degrees.

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J