Andy C. answered • 09/12/18

Math/Physics Tutor

So it will stand to reason then after a bit of thought that

the missing phrase should read:

" The measure of the third angle is 15 less than twice the sum of

the FIRST AND SECOND angles"

It's the only angle left that can be added....

Reading the problem, which angle do we know the LEAST about?

Which angle are we told nothing about?

"One angle of a triangle measure 5 more than three times the second angle" <--- we know something about the 1st angle

The measure of the third angle is 15 less than twice the sum of the first angle and 2nd angles",

so we know something about the 3rd angle

We know NOTHING about second angle. THAT is where you assign the variable

X is the measure of the 2nd angle.

the first angle is 3x + 5

the 3rd angle is 2(3x+5 +x ) - 15 <--- 15 less than twice the sum of the first and 2nd

2(4x + 5) - 15

8x + 10 - 15

8x - 5

The total of the angles must be 180

8x-5 + 3x+5 + x = 180

12x = 180

x = 180/12 = 15

2nd angle is 15

1st angle is 3(15)+5 = 45 + 5 = 50

3rd angle is 2(50+15) - 15 = 2(65) - 15 = 130 - 15 = 115

Yes, they total 180