Find the measures of the three angles of a triangle if the sum of the measure of the first angle and twice the

Question

Find the measures of the three angles of a triangle if the sum of the measure of the first angle and twice the measure of the second angle 15 degrees more than the measure of the third angle.

Show the steps so I can follow what you did, thanks.

Answer 1

You have two equations and three unknowns:

The angles must all add up to 180 degrees, so the first equation is:
a + b + c = 180

The other equation is:
a + 2b = c + 15

Let's arbitrarily pick a value for a of 15:

b + c =165
2b- c = 0
3b = 165
b = 55
c = 110

So one set of possible answers is 15, 55, 110

But let's try another value of a, say 30:
b + c =150
2b- c = -15
3b = 135
b = 45
c = 105

So another answeris 30, 45, 105

You could keep going with an infinite number of answers... are you sure you didn't miss something in the problem? Perhaps there's diagram and one of the angles is a right angle?