Question 215983
The second angle of a triangle is fifty less than four times the first angle. The third angle is forty less than the first. Find the measures of the three angles.


Step 1.  Let x be the first angle and 4x means 4 times the first angle.


Step 2.  Let 4x-50 be the second angle


Step 3.  Let x-40 be the third angle.


Step 4.  Sum of the angles in a triangle is 180 degrees.


Step 5.  Adding up the three angles is {{{x+4x-50+x-40=180}}}.  Solving yields the following steps.


{{{x+4x-50+x-40=180}}}


{{{6x-90=180}}}


Add 90 to both sides of the equation


{{{6x-90+90=180+90}}}


{{{6x=270}}}


Divide 6 to both sides of the equation


{{{6x/6=90/6}}}


{{{x=45}}}


Then {{{4x-50=180-50=130}}} and {{{45-40=5}}}.


Step 6.  ANSWER.  The angles of the triangle are 45, 130, and 5.   


Note=45+130+5=180 which is a true statement.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J