SOLUTION: Question 1 options: The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is three times the measure of the first angl

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Question 1196064: Question 1 options:
The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is three times the measure of the first angle. The third angle is fifteen more than the second. Find the measures of the three angles.
Answer by greenestamps(13203) (Show Source):
You can put this solution on YOUR website!

Since the problem is about the measures of three angles, you could solve the problem using three variables. That would mean you need three equations based on the given information.

But the algebra required to solve the problem is nearly always much easier if you take the time and effort at the start to use the given information to set up the problem using a single variable. So here is how I would solve the problem.

x = measure of 2nd angle
x+15 = measure of 3rd angle (15 more than the second)
180-x-(x+15) = 165-2x = measure of 1st angle (180 minus the sum of the other two)

Then my equation is based on the piece of information I haven't used yet -- that the sum of the measures of the 2nd and third angles is 3 times the measure of the first:

ANSWERS:
2nd angle = x = 60
3rd angle = x+15 = 75
1st angle = 180-(60+75) = 45

And here is a very different way of solving the problem which makes the required algebra even easier, or even makes the use of algebra unnecessary.

Since the sum of the measures of the 2nd and 3rd angles is 3 times the measure of the 1st, the 1st angle is 1/4 of the total of 180 degrees, so the 1st angle is 45 degrees.

That leaves 135 degrees for the sum of the measures of the 2nd and 3rd angles. And knowing that the 3rd angle is 15 more than the 2nd, you might not even need algebra to determine that the 2nd angle is 60 and the 3rd is 75.