Question 215469
If the sum of all angles in a triangle equal to 180, and the largest angle measures 10 degrees less than the sum of the other two angles; and a different angle is the average of the other two, what are the measurements of all three angles? 


Step 1.  Let x be one angle, y be the another angle


Step 2.  Let {{{x+y-10}}} since the largest angle measures 10 degrees less than the sum of the other two angles.


Step 3.  Let {{{x=(y+x+y-10)/2}}} since a different angle is the average of the other two.  Note the largest angle is included in the average. So if we solve for x then the other angle is y is added to the largest angle when conducting the average.   Simplifying yields {{{2x=2y+x-10}}} or {{{x-2y=-10}}}


Step 4.  {{{x+y+x+y-10=180}}} or {{{2x+2y=190}}} since adding the three angles equals to 180


Step 5.  Solve the system of equations shown below using substitution


{{{x-2y=-10}}}
{{{2x+2y=190}}}


*[invoke linear_substitution "x", "y", 1, -2, -10, 2, 2, 190 ]

With x=60 and y=35 then 180-35-60=85.


Now check for consistency.


85=x+y-10=60+35-10 for the largest triangle which is a true statement


x=60=(35+60)/2 which is also a true statement.


Step 6.  The three angles are 35, 60, and 85 degrees


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J