SOLUTION: one angle of a triangle is 5 degrees greater than the smallest angle, and the third angle is 45 degrees less than than twice the smallest angle. what is the measurements of the thr

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Question 221031: one angle of a triangle is 5 degrees greater than the smallest angle, and the third angle is 45 degrees less than than twice the smallest angle. what is the measurements of the three angles?
Answer by drj(1380) About Me  (Show Source):
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one angle of a triangle is 5 degrees greater than the smallest angle, and the third angle is 45 degrees less than than twice the smallest angle. What is the measurements of the three angles?

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

Step 2. Let x be the smallest angle.

Step 3. Let x+5 be the angle that is 5 degrees greater than the smallest angle.

Step 4. Let 2x-45 be twice the smallest angle.

Step 5. Then, x%2Bx%2B5%2B2x-45=180. Solving yields,

4x-40=180

Add 40 to both sides of the equation yields

4x-40%2B40=180%2B40

4x=220

Divide by 4 to both sides of the equation

4x%2F4=220%2F4

x=55. Then 2x-45=65 and x%2B5=60

Check 55+65+60=180 which is a true statement.

Step 6. The angles are 55, 65 and 60.

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J