The measure of the third angle is 40 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 40 degrees more than that of the smallest angle. Find the measure of the LARGEST angle.

Answer: The LARGEST angle has a measure of degrees.

Answer 1

Treena,

There are three variables here:

Smallest angle: x

Next angle: 3x

Final angle: x+40

All of the angles of a triangle add to 180 degrees, so we can create an equation:

180=x+3x+x+40

180=5x+40

140=5x

28=x

Now we plug this number into our two other angles, in order to solve for all measurements:

3x

3(28)

84 degrees

x+40

28+40

68 degrees

In order to check our answers, we will add all the measures together, to ensure that they are 180 degrees:

28+84+68=180 degrees!

The largest of the three angles is 84 degrees