Bunuel wrote:
Note: Figure not drawn to scale.
In the figure above, what is the measure of ∠ BED?
A. 40°
B. 55°
C. 65°
D. 80°
E. It cannot be determined from the information given.
Attachment:
2015-12-29_1841.png
In \(\triangle\)BED ,
\(\angle\) BED = 180 - (75+x ) = 105 - x
In \(\triangle\) FEC ,
\(\angle\) FEC = 180 - (85 +x ) = 95 -x
Since BEC is a straight line ,
\(\angle\) DEF= 180 - (105 - x + 95 -x)
= 2x- 20 -- 1
Also in\(\triangle\) DEF ,
\(\angle\) DEF = 180 -2x -- 2
From equations 1 and 2 , we get
4x = 200
=> x = 50
Now \(\angle\) BED = 105 - 50 = 55
Answer B
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