Question 215330
In Triangle ABC, Angle B is 8 less then one-half of angle A and angle C is 28 larger than angle A. Find the measure of the three angles of the triangle.


Step 1.  The three angles of triangle add up to 180 degrees.


Step 2.  Given angle {{{A}}}, then let {{{A/2-8}}} be angle B, and let {{{A+28}}} be angle C


Step 3.  Then,  add up all the angle to get 180 degrees or {{{A+A/2-8+A+8=180}}}.  Multiply by 2 to both sides of equation to get rid of denominator.


{{{2*(A+A/2-8+A+28)=2*180}}}


{{{2A+A-16+2A+56)=360}}}


{{{5A=320}}}


{{{A=64}}} 


With {{{A=64}}}, then {{{B=A/2-8=64/2-8=32-8=24}}} and {{{C=A+8=64+28=92}}}


Then A+B+C=180 as a check.  So 64+24+92=180 or 180=180 which is a true statement.


Step 4.  The angles are A=64 degrees, B=24 degrees, and C=92 degrees.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J