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

99 degrees

Explanation:

Break it down:

• The 3 angles of a triangle ALWAYS add up to 180
• Define one of the angles as a variable, call it x
• Write the expressions for the other two angles in terms of x
• Add them together and set equal to 180

"One angle is three times as large as the smallest angle."

Sounds like if we let x = "smallest angle", then 3x that is this angle.

"3rd angle is 15 degrees more that the smallest angle."

That sounds like "x + 15.

Now add them up:

x + 3x + (x + 15) = 180

See how there are three angles there? There's the smallest one, x. Another one, which is 3 times bigger than x. And another one, which is 15 degrees bigger than x. And we know because it's a triangle that all those angles have to add up to 180 degrees.

Now simplify and solve for x:

x + 3x + x + 15 = 180

5x = 165

x = 33 degrees

But is that the answer? No! They want the largest angle. Hmmm, that's probably going to be the one that's 3 times bigger, don't you think? So:

largest angle = 3 x 33 = 99 degrees

But always check your work. What's the third angle? 33 + 15 = 48 degrees. Now add up the 3 angles and see if they equal 180:

33 + 99 + 48 = 180 So yes, our answer is correct.