SOLUTION: In quadrilateral ABCD, angle A + angle C is 2 times angle B + angle D. If angle A = 40, then angle B =
(A) 60
(B) 80
(C) 120
(D) 240
(E) It cannot be determined from
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Question 309139: In quadrilateral ABCD, angle A + angle C is 2 times angle B + angle D. If angle A = 40, then angle B =
(A) 60
(B) 80
(C) 120
(D) 240
(E) It cannot be determined from the information given.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You don't have enough information to determine the measure of angle B. Here's why:
Since this is a quadrilateral, the sum of the interior angles is:
180^\circ\ =\ 360^\circ)
Hence:
Eq. 1: 
We also know that
And that
)
which is to say
Substituting for 
in Eq. 1:
And we then know that
from which we can determine that
But the only thing we know beyond that is that:
And from that we can deduce that:
But whether that is 
or 
or any other positive number less than 
we have no idea.
John
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