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 15 degrees more than that of the smallest angle.

Question

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 15 degrees more than that of the smallest angle. Find the measure of the LARGEST angle.

Answer 1

So since we are working with a Triangle, we know the sum of all three angles with be 180 degrees. In every triangle, the sum of all angles is 180 degrees.

So let's do it like this:

Let's say our smallest angle is n, okay?

Our second angle is 3n because it is 3 times as large as the smallest angle

And our third angle n + 15 because it's 15 degrees more than the smallest.

So since the sum is 180 we make an equation of: n + 3n + n + 15 = 180

We combine all like terms as well: 5n + 15 = 180

Now we solve for n by subtracting 15 on both sides: 5n = 165

And then we divide by 5 on both sides: n = 33

Now we have the measurement of our small angle which is 33 (because we said our smallest angle was n)

Now we plug in for our other two angles. Our second angle was 3n so it really is: 3 x 33 which is 99

And our third angle was 15 more than the smallest angle, so: 33 + 15 =48

Now we have our three angle measurements of 33, 99, and 48

And our Largest Measurement was 99

Really Hope this Helped!!