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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
Lets call the two angles x and y. One of them is 15 + half of the other one. Written as an equation, this says x+=+15+%2B+y%2F2+ (eq1).
Since they are complimentary, we know that the angles add up to 90 degrees. Thus x+%2B+y+=+90. We can rewrite this as x+=+90+-+y (eq2).
Now (eq2) gives us an equation for x that we can substitute into (eq1).
x+=+90+-++y+=+15+%2B+y%2F2.
+90+-+y+=+15+%2B+y%2F2+
Add y to both sides to get
+90+=+15+%2B+3y%2F2+
Subtract 15 from both sides to get
+75+=+3y%2F2+
Multiply both sides by 2 to get
+150+=+3+y
Divide both sides by 3 to get
+50++=+y+
Thus, from (eq2), we know that x=90-y=90-50=40
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