Question 227900
The second angle of a triangle is three times the first and the third is 12 degrees less than twice the first.  Find the measures of the angles. 


Step 1.  Let x be the first angle.


Step 2.  Let 3x be the second angle since it's three times the first.


Step 3.  Let 2x-12 be the third angle since it's 12 degrees less than twice the first.


Step 4.  We note that the sum of the three angles of a triangle is equal to 180 degrees. Then, x+3x+2x-12=180 or 6x=180+12=192.


Step 5.  Solving yields the following steps.


{{{6x=192}}}


Divide by 6 to both sides of the equation


{{{6x/6=192/6}}}


{{{x=32}}}  {{{3x=96}}} and {{{2x-12=64-12=52}}}


Check if angles equal to 180 degrees:  {{{32+96+52=180}}} which it does.


Step 6.  ANSWER:  The first angle is 32 degrees, the second angle is 96 degrees, and the third angle is 52 degrees.


I hope the above steps were helpful.


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And good luck in your studies!


Respectfully,
Dr J

http://www.FreedomUniversity.TV