Question 228468
One angle of a triangle is 35 degrees greater than the smallest angle and the third angle is 15 degrees less than twice the smallest angle. Find the measures of the 3 angles.


Step 1.  The sum of the three angles for a triangle is 180 degrees.


Step 2.  Let x be the smallest angle.


Step 3.  Let x+35 be the second angle since it's 35 degrees greater than the smallest angle.


Step 4.  Let 2x-15 be the third angle since it is 15 degrees less than twice the first.


Step 5.  Then, {{{x+x+35+2x-15=180}}} since the sum of the angles is 180 degrees.


Step 6.  Solving the equation {{{x+x+35+2x-15=180}}} yields the following steps


{{{4x+20=180}}}


Subtract 20 from both sides of the equation


{{{4x+5-5=180-20}}}


{{{4x=160}}}


{{{x=40}}} {{{x+35=75}}} and {{{2x-15=65}}}.  Note these three angles add up to 180 degrees as a check.


Step 6.  ANSWER:  The angles of the triangle are 40, 75, and 65 degrees.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J