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Find the largest angle of quadrilateral ABCD in degrees, if (angle A)/2 = (angle B)/3 = (angle R)/4.

Mar 8, 2020

#1
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We want the angles to form an arithmetic progression, so they are 36, 72, 108 144 degrees.  The largest angle is then 144 degrees.

Mar 9, 2020
#2
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No, that is incorrect. Although it does seem reasonable and they add up to 360, one half of 36 doesn't equal a third of 72, etc.

Unless, of course, you can prove me wrong.

Guest Mar 9, 2020
#3
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Find the largest angle of quadrilateral ABCD in degrees, if (angle A)/2 = (angle B)/3 = (angle R)/4. ( R is C )

(Angle A)/2  => 48 / 2 = 24

(Angle B)/3  => 72 / 3 = 24

(Angle C)/4  => 96 / 4 = 24

The largest angle D = 360 - 48 - 72 - 96 = 144º Mar 9, 2020
#4
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So basically I accidentally rigged the odds against you and the question was missing one critical piece of information.

The quadrilateral is cyclic. Which means you can inscribe it in a circle.

See if you can solve it again.

Actually I'm too lazy to wait so basically the opposite angles of a cyclic quadrilateral are supplementary, so angle A plus angle C is equal to 180. And, A plus C is 6 of those "units," so the missing angles must be 3 of them. So, since C has 4 of them, that is the largest angle. Since we have split up the quadrilateral into 12 of those units, each is 30 degrees. Therefore, 30*4=120.

Sorry

Big apologies

But in the end, we're both anonymous so no one actually cares. Guest Mar 10, 2020
#5
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No problem, guest. That question is now even more interesting. Guest Mar 10, 2020