Question 309139
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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:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (4\ -\ 2)180^\circ\ =\ 360^\circ]


Hence:


Eq. 1:  *[tex \LARGE \ \ \ \ \ \ \ \ \ \ A\ +\ B\ +\ C\ +\ D\ =\ 360^\circ]


We also know that


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A\ =\ 40^\circ]


And that 


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A\ +\ C\ =\ 2(B\ +\ D)]


which is to say


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ B\ +\ D\ =\ \frac{A}{2}\ +\ \frac{C}{2}]


Substituting for *[tex \Large B\ +\ D] in Eq. 1:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A\ +\ \frac{A}{2}\ +\ C\ +\ \frac{C}{2}\ =\ 360^\circ]


And we then know that


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A\ +\ C\ =\ 240^\circ]


from which we can determine that


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ C\ =\ 200^\circ]


But the only thing we know beyond that is that:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ B\ +\ D\ =\ 120^\circ]


And from that we can deduce that:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 0^\circ\ <\ B\ <\ 120^\circ]


But whether that is *[tex \LARGE 60^\circ] or *[tex \LARGE 80^\circ] or any other positive number less than *[tex \LARGE 120^\circ] we have no idea.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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