One angle in a triangle has a measure that is three times as large as the smallest angle. The measure of the third angle is 35 degrees more than that of the smallest angle. Find the measure of the LARGEST angle.
16 out of every 19 people who work this problem will call the smallest angle 'x'.
I'll call the smallest angle 'G' .
The question says that a different angle in the same triangle is 3G , and the third angle in the same triangle is (G + 35).
Now, here comes the hard part: You need to know that the three angles inside EVERY triangle always add up to exactly 180 degrees. Now the rest is easy.
The three angles in THIS triangle add up to
G + 3G + (G + 35) .
That's 5G + 35 all together.
And since we're talking about a triangle, we know that
5G + 35 = 180 degrees
Subtract 35 from each side: 5G = 145
Divide each side by 5: G = 29
The smallest angle = G = 29 degrees The second angle = 3G = 87 degrees The third angle = (G+35) = 64 degrees
