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# In the diagram below, what is the measure of ∠BCD?

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Math Expert
Joined: 02 Sep 2009
Posts: 50583
In the diagram below, what is the measure of ∠BCD?  [#permalink]

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24 Jul 2017, 22:17
00:00

Difficulty:

15% (low)

Question Stats:

87% (00:59) correct 13% (01:25) wrong based on 84 sessions

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In the diagram below, what is the measure of ∠BCD?

(1) AB is parallel to DE.
(2) ∠ABC = 55°.

Attachment:

2017-07-25_1016.png [ 3.35 KiB | Viewed 1943 times ]

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Re: In the diagram below, what is the measure of ∠BCD?  [#permalink]

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25 Jul 2017, 00:01
Bunuel wrote:
In the diagram below, what is the measure of ∠BCD?

(1) AB is parallel to DE.
(2) ∠ABC = 550.

Attachment:
2017-07-25_1016.png

Hi Bunuel

is ∠ABC = 550 correct..i suppose it will be ∠ABC = 55 Degree
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Re: In the diagram below, what is the measure of ∠BCD?  [#permalink]

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25 Jul 2017, 00:07
Assuming angle ABC is 55 the answer will be 90+(180-55)=215

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Re: In the diagram below, what is the measure of ∠BCD?  [#permalink]

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25 Jul 2017, 00:12
mynamegoeson wrote:
Bunuel wrote:
In the diagram below, what is the measure of ∠BCD?

(1) AB is parallel to DE.
(2) ∠ABC = 550.

Attachment:
2017-07-25_1016.png

Hi Bunuel

is ∠ABC = 550 correct..i suppose it will be ∠ABC = 55 Degree

It's 55°. Edited. Thank you.
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Re: In the diagram below, what is the measure of ∠BCD?  [#permalink]

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27 Jul 2017, 04:55
Is it C??

Since both statements would be required to measure the angle BCD
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In the diagram below, what is the measure of ∠BCD?  [#permalink]

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07 Nov 2017, 10:15
Let $$\angle BCD = x$$

Using statement 1:

From the new diagram attached, you can extend BC to intersect DE at a new point, say F.
The angle formed, i.e $$\angle CFD = \angle ABC = y$$

In triangle CFD, $$\angle CDF = 90 \angle FCD = 180 -x$$
180 - x + y + 90 = 180
x-y = 90

Hence 1 is insufficient.

Statement 2 gives us $$\angle ABC$$ but we dont know if AB and DE are ||

Using 1 and 2, we can find $$\angle BCD = 180 - 35 = 145$$
Attachments

slice1.png [ 10.69 KiB | Viewed 1257 times ]

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In the diagram below, what is the measure of ∠BCD? &nbs [#permalink] 07 Nov 2017, 10:15
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