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

Answer:

24, 72, and 84

Step-by-step 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