Question 214210
The measures of two supplementary angles are in the ratio 2:3. Find their measures.


Step 1.  Let 2x be one angle and 3x be the other angle.  The ratio of these two angles is 2x/3x=2/3 as given on the problem.


Step 2.  The two angles must add up to 180 degrees by definition.


Step 3.  Then 2x+3x=180 or 5x=180 which implies that x=36. 2x=72  and 3x=108


Step 4.  The angles are then 72 degrees and 108 degrees.  Note the two angles add up to 180 and their ratio is 72/108=2/3 satisfying the problem statement.


I hope the above steps were helpful. 


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And good luck in your studies!


Respectfully,
Dr J