Question 221389
In triangle ABC, angle A is twice as large as angle B. Angle B is 4 degrees larger than Angle C. Find the measure of each angle.


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


Step 2.   Let B=C+4 since Angle B is 4 degrees larger than Angle C.


Step 3.  Let A=2B=2(C+4) since Angle A is twice as large as angle B.


Step 4.  Then A+B+C=2(C+4)+C+4+C=180 


Step 5.  Simplifying equation in Step 4 yields the following steps.


{{{2(C+4)+C+4+C=2C+8+2C+4=180}}}


{{{4C+12=180}}}


Subtract 12 from both sides


{{{4C+12-12=180-12}}}


{{{4C=168}}}


Divide by 4 to both sides of the equation


{{{4C/4=168/4}}}


{{{C=42}}} {{{B=C+4=46}}} and {{{A=2B=2*46=92}}}


Check if A+B+C=180 or 42+46+92=180...a true statement.


Step 6.  ANSWER:  Angle A is 92 degrees, Angle B is 46 degrees and Angle C is 42 degrees.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J