Question 228463
The second angle of a triangle is four times the first and the third is 5 degree more than twice the first. Find the measures of the angle.


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


Step 2.  Let x be the first angle.


Step 3.  Let 4x be the second angle since it's four times the first.


Step 4.  Let 2x+5 be the third angle since it is 5 degrees more than twice the first.


Step 5.  Then, {{{x+4x+2x+5=180}}} since the sum of the angles is 180 degrees.


Step 6.  Solving the equation {{{x+4x+2x+5=180}}} yields the following steps


{{{7x+5=180}}}


Subtract 5 from both sides of the equation


{{{7x+5-5=180-5}}}


{{{7x=175}}}


{{{x=25}}} {{{4x=100}}} and {{{2x+5=55}}}.  Note these three angles add up to 180 degrees as a check.


Step 6.  ANSWER:  The angles of the triangle are 25, 100, and 55 degrees.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J