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find the measure of two complementary angles if 8 times the measure of one is 31* more than 5 times the measure of the other.

A) 37*, 63* C) 73*, 17*
B) 37*, 53* D) 73*, 107*

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We know it's not A or D because they do not add up to 90. That makes it easier because now all you hafta do is make an equation, and plug in the values from B and C, and see which work out. So let one of the complementary angles be X, and the other is Z.
8x= 5z + 31 } = 90
8(37) = 5(53) + 31
296 = 296
So the answer is B, but you can check C also if you want (I made 37 X instead of Z because it is smaller, so I figured that multiplied by 8 would be around the same as 53 multiplied by 5 plus 31) Comment if you have any questions! This was more of an algebra problem than a geometry one.

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It's 90, and you're right it does eliminate 2 of the answers!
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for starters, complimentary angles add up to equal 90 degrees (x+y=90). so right there you can eliminate two of your answers (A and D). then you need to set it up so the you have an equation. one angle on each side. so your equation would be 8x=5y+31. from here solve for x by dividing the side with y by 8. so x=(5y+31)/8 now. you take what x equals( the equation) and . which should give you ((5y+31/8)+y=90. and solve for y.

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X=1st angle
90-x= it's comp
8(x)=5(90-x)+31
These are fairly basic geom problems which you should learn to work by hand.