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In the figure shown, if the measure of angle BAD is 60 degrees, ABCD

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

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New post 27 May 2018, 10:02
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Question Stats:

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

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

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

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New post 28 May 2018, 06:22
1
Bunuel wrote:
Image

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

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New post 28 May 2018, 07:45

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.

Answer: 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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New post 22 Aug 2019, 18:05
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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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