SOLUTION: one of 2 complementary angles measures 15 degree increased by half of the other. find the measure of both angles.

Question 316144: one of 2 complementary angles measures 15 degree increased by half of the other. find the measure of both angles.

Answer by moshiz08(60) (Show Source): You can put this solution on YOUR website!
Lets call the two angles and . One of them is 15 + half of the other one. Written as an equation, this says (eq1).
Since they are complimentary, we know that the angles add up to 90 degrees. Thus . We can rewrite this as (eq2).
Now (eq2) gives us an equation for that we can substitute into (eq1).
.

Add y to both sides to get

Subtract 15 from both sides to get

Multiply both sides by 2 to get

Divide both sides by 3 to get

Thus, from (eq2), we know that
Now we check: 40 and 50 do add up to 90, so they are complimentary.
Also, one of them is 15 plus half of the other since
15 + half of 50 = 15 + 25 = 40
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