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# In the figure above, the measure of angle CAE is equal to the measure

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Math Expert
Joined: 02 Sep 2009
Posts: 60627
In the figure above, the measure of angle CAE is equal to the measure  [#permalink]

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19 Jul 2017, 03:00
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Difficulty:

15% (low)

Question Stats:

88% (00:44) correct 13% (01:19) wrong based on 55 sessions

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In the figure above, the measure of angle CAE is equal to the measure of angle BAD. Which of the following must be true?

(A) x = y
(B) y = z
(C) x = z
(D) x = y = z
(E) none of the above

Attachment:

2017-07-19_1358.png [ 9.87 KiB | Viewed 2099 times ]

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Posts: 239
GPA: 3.57
Re: In the figure above, the measure of angle CAE is equal to the measure  [#permalink]

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19 Jul 2017, 03:56
Bunuel wrote:

In the figure above, the measure of angle CAE is equal to the measure of angle BAD. Which of the following must be true?

(A) x = y
(B) y = z
(C) x = z
(D) x = y = z
(E) none of the above

Attachment:
2017-07-19_1358.png

It should be C.

A - Only true if AD bisects CAE and we do not know that from the figure.
B - Only true if AC bisects BAD and we do not know that.
C - True
D - Uncertain for the same reasons as A and B.
E - NA.
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Joined: 22 May 2016
Posts: 3725
In the figure above, the measure of angle CAE is equal to the measure  [#permalink]

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19 Jul 2017, 07:47
Bunuel wrote:

In the figure above, the measure of angle CAE is equal to the measure of angle BAD. Which of the following must be true?

(A) x = y
(B) y = z
(C) x = z
(D) x = y = z
(E) none of the above

Attachment:
2017-07-19_1358.png

x + y = Angle CAE
z + y = Angle BAD

x + y = z + y, subtract y from both

x = z

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Posts: 1868
Re: In the figure above, the measure of angle CAE is equal to the measure  [#permalink]

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19 Jul 2017, 09:25
Bunuel wrote:

In the figure above, the measure of angle CAE is equal to the measure of angle BAD. Which of the following must be true?

(A) x = y
(B) y = z
(C) x = z
(D) x = y = z
(E) none of the above

Attachment:
2017-07-19_1358.png

Hence x + y = y + z

Therefore x = z

Correct Option: C
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Joined: 21 Mar 2016
Posts: 494
Re: In the figure above, the measure of angle CAE is equal to the measure  [#permalink]

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19 Jul 2017, 22:53

x + y = Z + y

x = z
ans C
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Joined: 04 Mar 2011
Posts: 2806
Re: In the figure above, the measure of angle CAE is equal to the measure  [#permalink]

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25 Jul 2017, 10:52
Bunuel wrote:

In the figure above, the measure of angle CAE is equal to the measure of angle BAD. Which of the following must be true?

(A) x = y
(B) y = z
(C) x = z
(D) x = y = z
(E) none of the above

Since angle CAE = angle BAD:

y + x = z + y

x = z

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Re: In the figure above, the measure of angle CAE is equal to the measure   [#permalink] 25 Jul 2017, 10:52
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