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555-605 (Medium)|   Geometry|      
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Bunuel
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In the figure, ABCD is a square and BCP is an equilateral triangle. Wh Updated on: 22 Jul 2019, 06:24
Originally posted by Bunuel on 02 Apr 2019, 23:34.
Last edited by Sajjad1994 on 22 Jul 2019, 06:24, edited 1 time in total.
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

25% (medium)

Question Stats:

79% (02:17) correct 21% (02:10) wrong based on 157 sessions

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In the figure, ABCD is a square and BCP is an equilateral triangle. What is the measure of x ?

(A) 7.5

(B) 15

(C) 30

(D) 45

(E) 60

Source: Nova GMAT
Difficulty Level: 600
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#GREpracticequestion In the figure, ABCD is a square.jpg
#GREpracticequestion In the figure, ABCD is a square.jpg [ 31.21 KiB | Viewed 9917 times ]
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C
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In the figure, ABCD is a square and BCP is an equilateral triangle. Wh 03 Apr 2019, 07:03
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Bunuel

In the figure, ABCD is a square and BCP is an equilateral triangle. What is the measure of x ?

(A) 7.5

(B) 15

(C) 30

(D) 45

(E) 60

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Attachment:
#GREpracticequestion In the figure, ABCD is a square.jpg
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solve
∆ADP
90-y+90-y+x=180
or say x= 2y
plugin given options
starting x= 30
so y=15
so
75+75+30 = 180
sufficient
IMO C
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In the figure, ABCD is a square and BCP is an equilateral triangle. Wh 04 Apr 2019, 18:33
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Bunuel

In the figure, ABCD is a square and BCP is an equilateral triangle. What is the measure of x ?

(A) 7.5

(B) 15

(C) 30

(D) 45

(E) 60

Show Spoiler
Attachment:
#GREpracticequestion In the figure, ABCD is a square.jpg
Show more

Since PC = DC, we see that triangle PCD is an isosceles triangle. We see that angle PCD = 60 + 90 = 150 degrees. Using triangle PCD, we have:

2y + 150 = 180

2y = 30

y = 15

So angle DPC = 15 degrees, and we can see that angle BPA = 15 degrees. Since angle BPC = 60 degrees, then angle APD, or x, is 60 - 2(15) = 30 degrees.

Answer: C
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In the figure, ABCD is a square and BCP is an equilateral triangle. Wh 10 May 2019, 17:34
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ScottTargetTestPrep
Bunuel

In the figure, ABCD is a square and BCP is an equilateral triangle. What is the measure of x ?

(A) 7.5

(B) 15

(C) 30

(D) 45

(E) 60

Show Spoiler
Attachment:
#GREpracticequestion In the figure, ABCD is a square.jpg

Since PC = DC, we see that triangle PCD is an isosceles triangle. We see that angle PCD = 60 + 90 = 150 degrees. Using triangle PCD, we have:

2y + 150 = 180

2y = 30

y = 15

So angle DPC = 15 degrees, and we can see that angle BPA = 15 degrees. Since angle BPC = 60 degrees, then angle APD, or x, is 60 - 2(15) = 30 degrees.

Answer: C
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Hello ScottTargetTestPrep!

How do we know that PC = DC?

Kind regards!
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In the figure, ABCD is a square and BCP is an equilateral triangle. Wh 13 May 2019, 10:36
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jfranciscocuencag
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Bunuel

In the figure, ABCD is a square and BCP is an equilateral triangle. What is the measure of x ?

(A) 7.5

(B) 15

(C) 30

(D) 45

(E) 60

Show Spoiler
Attachment:
#GREpracticequestion In the figure, ABCD is a square.jpg

Since PC = DC, we see that triangle PCD is an isosceles triangle. We see that angle PCD = 60 + 90 = 150 degrees. Using triangle PCD, we have:

2y + 150 = 180

2y = 30

y = 15

So angle DPC = 15 degrees, and we can see that angle BPA = 15 degrees. Since angle BPC = 60 degrees, then angle APD, or x, is 60 - 2(15) = 30 degrees.

Answer: C

Hello ScottTargetTestPrep!

How do we know that PC = DC?

Kind regards!
Show more

Since ABCD is a square, all the sides have equal length. Since BCP is an equilateral triangle, all sides of BCP have equal length as well. Finally, since one side of ABCD and BCP are common, all sides of the square and the triangle BCP have equal length. Since PC is a side of BCP and and DC is a side of the square, they have equal length.

If that was hard to follow, you can start labeling the lengths of the sides of the square, say all sides have length l. Then, continue labeling the lengths of the sides of the equilateral triangle. In the end, you'll see that both PC and DC are labeled l.
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In the figure, ABCD is a square and BCP is an equilateral triangle. Wh 18 Dec 2024, 12:54
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