SOLUTION: the ratoio of the supplementary angle and the complementary angle of an angle is 8:3 .find the angle

Question 720849: the ratoio of the supplementary angle and the complementary angle of an angle is 8:3 .find the angle

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
If you have two unknown numbers but you know what they add up to, then a single variable can be used to express both unknowns. For example, if two unknown numbers add up to 100, then use "x" for one number. The other number will be (100-x). This is a good thing to know when solving word problems. The fewer variables you use, the easier the solution will be.

We can use this in solving your problem. Supplementary angles are two angles that add up to 180 degrees. So if "an angle" is "x", then the supplementary angle would be (180-x). Complementary angles are two angles that add up to 90 degrees. So if "an angle" is still "x", then the complementary angle would be (90-x).

We are told that the ratio of these the supplementary and complementary angles is 8:3. So:

Since we used just one variable, we can solve the problem with this one equation. (If we had used two variables we would need two equations. If we had used three variables we would need three equations.) Our equation is a proportion (one fraction equals another fraction) so we can use cross-multiplying:

Simplifying...

Adding 8x:

Subtracting 540:

Dividing by 5:

Since "x" was "an angle" it is the angle we were asked to find. (If we were asked to find the supplementary angle we would find 180 - x = 180 - 36 = 144. If we were asked to find the complementary angle we would find 90 - x = 90 - 36 = 54.)
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