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In the figure above, what is the measure of ∠ BED?

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In the figure above, what is the measure of ∠ BED?  [#permalink]

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New post 29 Dec 2015, 06:44
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Image
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
2015-12-29_1841.png [ 20.57 KiB | Viewed 2849 times ]

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In the figure above, what is the measure of ∠ BED?  [#permalink]

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New post 29 Dec 2015, 07:41
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Bunuel wrote:
Image
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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Re: In the figure above, what is the measure of ∠ BED?  [#permalink]

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New post 01 Jan 2016, 11:28
3
Hi All,

When a prompt notes that the figure is NOT drawn to scale, you have to be very careful about how you let the drawing 'influence' your decisions. You CAN trust the 'data' you're given (the numbers and variables), but you can't trust the 'scale' of the picture. That means that while the 4 triangles might 'look' like they're the same 4 triangles, they are almost certainly NOT.

One of the keys to answering this question quickly is to note that any 4-sides shape consists of 4 angles that total 360 degrees. Here, we can see a 4-sided shape that contains ALL of the Xs in the drawing: BCFD.

The 4 angles in BCFD are: 75, 85, 2X and 2X

So, 75+85+2X+2X = 360

160+4X = 360
4X = 200
X = 50

Since the question asks for the measure of angle BED, and BED is part of the 'top' triangle, we have...

75+50+(angle BED) = 180
125+(angle BED) = 180
angle BED = 55

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Re: In the figure above, what is the measure of ∠ BED?  [#permalink]

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New post 14 Jul 2016, 22:02
Bunuel wrote:
Image
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

There are many a ways one can solve it
Here is another approach from above two
∠A=20
Also in triangle ADF ,exterior ∠DFC(2x)=∠DAF+∠ADF=20+∠ADF=2x
∠ADF=2x-20-------(a)
Also segment ADB we have ∠ADF+∠FDE+∠EDB=180-----(b)
putting value of ∠ADF=2x-20-------from(a)
we can write (b) as
2x-20+x+x=180(from fig)
therefore x=50
Now in trialgle BDE sum of interior angle=180
we know ∠DBE=75 && ∠BDE=x=50
So ∠BED=180-(75+50)=55
Ans B
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Re: In the figure above, what is the measure of ∠ BED?  [#permalink]

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Re: In the figure above, what is the measure of ∠ BED? &nbs [#permalink] 12 Sep 2018, 15:11
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