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

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Math Expert
Joined: 02 Sep 2009
Posts: 50621
In the figure above, what is the measure of ∠ BED?  [#permalink]

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29 Dec 2015, 06:44
00:00

Difficulty:

45% (medium)

Question Stats:

70% (02:39) correct 30% (02:31) wrong based on 95 sessions

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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 [ 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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29 Dec 2015, 07:41
3
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

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

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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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14 Jul 2016, 22:02
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

There are many a ways one can solve it
Here is another approach from above two
∠A=20
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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12 Sep 2018, 15:11
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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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