Question 229572
The measure of 2 supplementary angles are represented by (3x+10)degrees and (7x-40)degrees.  Can you help me understand how to determine the measure of each angle?


Step 1.  Two angles are supplementary when they add up to 180 degrees.


Step 2.  Then (3x+10)+(7x-40)=180. 


Step 3.  Solving (3x+10)+(7x-40)=180 yields the following steps


Add like terms


{{{(3x+7x)+(10-40)=180}}}


{{{10x-30=180}}}


Add 30 to both sides of the equation to get numbers only on one side and variables on the other side.


{{{10x-cross(30)+cross(30)=180+30}}}


{{{10x=210}}}


Divide by 10 to both sides of the equation


{{{cross(10)x/cross(10)=210/10}}}


{{{x=21}}}  {{{3x+10=63+10=73}}} and {{{7x-40=147-40=107}}}.  Note the angles 73 and 107 add up to 180 degrees.


Step 4.  ANSWER:  The angles are 73 and 107 degrees.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J