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

Algebra ->  Polygons -> 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       Log On


   

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) About Me  (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:



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