Question 220958
Angle A and angle B are supplementary angles and angle A is 20 degrees less than four times angle B. Find the measure of angle A and Angle B.


Step 1.  Supplementary angles means two angles add up to 180 degrees.


Step 2.  So, B=180-A since B is supplementary to A


Step 3.  Let 4B=4(180-A) is four times the angle B.


Step 4.  A=4(180-A)-20 since angle A is less than four times angle B.


Step 5.  Solving yields the following steps


{{{A=4(180-A)-20}}}


{{{A=720-4A-20}}}


Adding 4A to both sides of the equation


{{{A+4A=700-4A+4A}}}


{{{5A=700}}}


Step 6.  Divide by 5 to both sides of the equation


{{{5A/5=700/5}}}


{{{A=140}}}  then {{{B=180-40=40}}} and note {{{140=4*40-20}}}...true statement.


Step 7.  The angles are A=140 and B=40


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J