Question

The measure of one angle of a triangle is three times the measure of a second angle. the measure of the third angle is 12 less than the sum of the other two. what are the measures of the 3 angles

PLEASEEEE HELP<333

Answer 1

24, 72, and 84

Explanation:

Let the first, second, and third angles be A, B, and C, respectively.

So, first of all, since the figure is a triangle, the three angles must total 180. Thus:

`A+B+C=180`

Now, we are told that the measure of one angle (let's use A) is 3 times the measure of a second angle (B). So:

`A=3B`

And the measure of the third angle (C) is 12 less than the sum of the other two (A&B). Therefore:

`C=(A+B)-12`

For this equation substitute A for 3B:

`C=(3B+B)-12`

Combine like terms:

`C=4B-12`

So we have the following equations thus far:

`A+B+C=180`

`A=3B`

`C=4B-12`

So, substitute A and C in for the first equation:

`A+B+C=180\\(3B)+B+(4B-12)=180`

Combine like terms:

`8B-12=180`

Add 12 to both sides:

`8B=192`

Divide by 8:

`B=24`

So, the second angle B is 24 degrees.

The first angle A is three times B. Thus, A is 3(24)=72 degrees.

And C is 12 less than the sum of them. Thus:

`C=(72+24)-12\\C=96-12\\C=84`

So, our angles are:

24, 72, and 84

And we are done :)

Edit: Typo