How do you find the measures of the angles of a triangle if the measure of one angle is twice the measure of a second angle and the third angle measures 3 times the second angle decreased by 12?

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Answer 1 · 2018-05-09T10:01:29

$/_A=32^@, /_B=64^@, /_C=84^@$

To be certain I understand your question correctly, you have a triangle, where you with "measures" mean number of degrees each angle is.

I.e. let the triangle look something like this:

enter image source here

If $/_A=a^@$
Then $/_B=2/_A=2a^@$
And $/_C=3/_A-12^@=3a^@-12^@$

If my understanding of your question is correct, we have
$/_A+/_B+/_C=180^@$
Therefore $a^@+2a^@+3a^@-12^@=180^@$

This gives $6a^@-12^@=180^@$
Or $a^@=32^@$

The angles in the triangle, therefore, are
I.e. $/_A=a^@=32^@$
Then $/_B=2/_A=2a^@=64^@$
And $/_C=3/_A-12^@=84^@$

This gives the following triangle:

enter image source here