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 measur…

Question

asked Aug 2, 2021 15.6k views

1 Answer

Amoffat · Answer 1 · 2021-08-06T13:53:05+0000

Answer:

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