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Math Expert V
Joined: 02 Sep 2009
Posts: 57993
In the figure shown, if the measure of angle BAD is 60 degrees, ABCD  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 65% (02:38) correct 35% (02:23) wrong based on 54 sessions

### HideShow timer Statistics In the figure shown, if the measure of angle BAD is 60 degrees, ABCD is a parallelogram, and line BC bisects line AE, what is the length of side EC?

(1) The length of DC is 12.
(2) The length of BC is 12.

Attachment: screen_shot_2011_01_06_at_12.27.16_pm.png [ 23.16 KiB | Viewed 693 times ]

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Senior PS Moderator V
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Re: In the figure shown, if the measure of angle BAD is 60 degrees, ABCD  [#permalink]

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1
Bunuel wrote: In the figure shown, if the measure of angle BAD is 60 degrees, ABCD is a parallelogram, and line BC bisects line AE, what is the length of side EC?

(1) The length of DC is 12.
(2) The length of BC is 12.

Attachment:
screen_shot_2011_01_06_at_12.27.16_pm.png

From the question stem, we can deduce the following information
1. In a parallelogram, the opposite sides are equal. Here, AB = CD and BC = AD.
2. Opposite angles are supplementary - angle CBA = 120.
3. CBE + CBA = 180 -> CBE = 180 - 120 = 60 degree

1. AB = 12. Since the line bisects AE, EB = BA = 12.
We have no idea about the length of BC and we can't come to a conclusion about
the length of EC. (Insufficient)

2. Knowing the length of BC alone is not enough to come to a conclusion about the
length of EC. (Insufficient)

Combining the information present in both the statements and the question stem,
we know that the triangle EBC is equilateral and EC = 12 (Sufficient - Option C)
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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3024
Re: In the figure shown, if the measure of angle BAD is 60 degrees, ABCD  [#permalink]

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Solution

Given:
In the given figure,
• Angle BAD = 60°
• ABCD is a parallelogram
• Line BC bisects line AE, i.e. AB = BE

To find:
• Length of the side EC

Analysing Statement 1
• As per the information provided in Statement 1, DC = 12
o From this, we can say AB = 12, as ABCD is a parallelogram
o We can also say BE = 12, as AB = BE
• But we cannot conclude anything about EC

Hence, statement 1 is not sufficient to answer

Analysing Statement 2
• As per the information provided in Statement 2, BC = 12
o From this, we can say AD = 12, as ABCD is a parallelogram
• But we cannot conclude anything about EC

Hence, statement 2 is not sufficient to answer

Combining Both Statements
If we combine the information available in both the statements, we can say,
• AB = BE = DC = BC = AD = 12
• Angle BAD = 60°
o Therefore, angle ABC = 180° - 60° = 120°
o Hence, angle EBC = 60°
• Now, in triangle EBC, as BE = BC, angle BEC = angle BCE = x (assuming)
o Therefore, we can write 60° + x + x = 180°
Or, x = 60°
• As all the angles of triangle EBC are equal to 60°, triangle EBC is a equilateral triangle, with side length 12
• Hence, EC = 12

Hence, the correct answer is option C.

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Re: In the figure shown, if the measure of angle BAD is 60 degrees, ABCD  [#permalink]

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_________________ Re: In the figure shown, if the measure of angle BAD is 60 degrees, ABCD   [#permalink] 22 Aug 2019, 18:05
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# In the figure shown, if the measure of angle BAD is 60 degrees, ABCD

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