need help working this out

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

Hello Gina,

Let's call the smallest angle x. Therefore:

1. "One angle in a triangle has a measure that is three times as large as the smallest angle" means that angle would have a measure of 3*x
2. "The measure of the third angle is 15 degrees more than that of the smallest angle" means the 3rd angle would have a measure of x + 15

So now, you have expressions for all 3 angles of the triangle: x , 3x, and x + 15

The sum of all angles in a triangle is 180 degrees, so: x + 3x + x + 15 = 180

If you add the x terms, you get: 5x + 15 = 180, which you can solve for x

Subtract 15 from both sides: 5x = 165

Divide both sides by 5: x = 165/5 = 33

So the SMALLEST angle x has a measure of 33 degrees. Let's go back to our two bullet points to find the remaining 2 angles:

1. "One angle in a triangle has a measure that is three times as large as the smallest angle" means that angle would have a measure of 3*x ----> 3*x = 3*33 = 99 so this angle is equal to 99 degrees
2. "The measure of the third angle is 15 degrees more than that of the smallest angle" means the 3rd angle would have a measure of x + 15 ----> 33 + 15 = 48 so this angle is equal to 48 degrees

99 + 48 + 33 = 180 degrees so the math checks out.

Now: your three angles are 33 degrees, 99 degrees and 48 degrees. I'll let you figure out which of these is the LARGEST angle and the problem is solved.

Cheers.