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Question 926825: The measures of two complementary angles are in the ratio 2:3. What is the measure of the smaller angles?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! angles are complementary so their sum is 90.
a equals one of the angles
b = the other angle.
the angles are in a ratio of 2/3.
a/b = 2/3
multiply both sides of the equation by b to get:
a = 2b/3
you have a + b = 90 because the angles are complementary.
you know that a = 2b/3
replace a with 2b/3 in the equation of a + b = 90 to get:
2b/3 + b = 90
since b is equivalent to 3b/3, the equation becomes:
2b/3 + 3b/3 = 90
combine fractions with the same denominator together to get:
5b/3 = 90
multiply both sides of the equation by 3 to get:
5b = 270
divide both sides of the equation by 5 to get:
b = 54 degrees.
since a = 2b/3, then a must be equal to 2*54/3 = 36 degrees.
a = 36 degrees
b = 54 degrees
a+b = 90 so the answer looks good.
the smaller angle measures 36 degrees.
another way to look at it.
angles are in a ratio of 2 to 3.
the sum of the angles will be x times each of them.
you get 2x + 3x = 90
this is because the angles are complementary and their sum is therefore equal to 90.
combine like terms to get 5x = 90
divide both sides of this equation by 5 to get x = 18.
the smaller angle is 2x = 2 times 18 = 36 degrees.
the larger angle is 3x = 3x = 3 * 18 = 54 degrees.
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