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In the figure, what is the value of x ?

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Bunuel
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In the figure, what is the value of x ? [#permalink] New post   03 Apr 2019, 23:14
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A
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25% (medium)

Question Stats:

79% (01:15) correct 21% (01:32) wrong based on 63 sessions
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In the figure, what is the value of x ?

(A) 90

(B) 95

(C) 100

(D) 105

(E) 115


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#GREpracticequestion In the figure, what is the value of x .jpg [ 27.41 KiB | Viewed 2303 times ]
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D
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LevanKhukhunashvili
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Re: In the figure, what is the value of x ? [#permalink] New post   04 Apr 2019, 00:07
3 things are necessary here

1) Opposite angles are the same;
2) Angles of the equilateral triangle;
3) Triangle with sides 3, 4, 5 is a right triangle as \(3^2+4^2=5^2\);

if you catch those 3 concepts quickly, you wont waste 7 minutes like me

After some smooth calculations, you get
360=60+90+2x
x=105

IMO
Ans: D
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Re: In the figure, what is the value of x ? [#permalink] New post   04 Apr 2019, 02:19
LHS is right angled we get 90* and RHS is equilaterlal ∆ 60*
so sum of quadrilaterial = 150+2x= 360
x= 105
IMO D


[

quote="Bunuel"]
In the figure, what is the value of x ?

(A) 90

(B) 95

(C) 100

(D) 105

(E) 115


Show Spoiler
Attachment:
#GREpracticequestion In the figure, what is the value of x .jpg
[/quote]
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Re: In the figure, what is the value of x ? [#permalink] New post   04 Apr 2019, 09:20
Who told you all that the leftmost triangle is a right triangle ?

thanks
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Re: In the figure, what is the value of x ? [#permalink] New post   04 Apr 2019, 09:21
testcracker wrote:
Who told you all that the leftmost triangle is a right triangle ?

thanks


testcracker
∆ with sides 3:4:5 is a right angled triangle ....
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Re: In the figure, what is the value of x ? [#permalink] New post   04 Apr 2019, 09:44
IMO D

triangle with sides 5 , 4 , 3 form a pythagoras triplet

25 = 16+9


hope this helps

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Re: In the figure, what is the value of x ? [#permalink] New post   04 Apr 2019, 09:51
Left most triangle is a right angle triangle
Right most triangle is an equilateral triangle= Each angle = 60
Sum of the angle of the middle figure =360
360 = 2x+60+90
x=105 i.e D
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Re: In the figure, what is the value of x ? [#permalink] New post   07 Apr 2019, 18:58
Expert Reply
Bunuel wrote:

In the figure, what is the value of x ?

(A) 90

(B) 95

(C) 100

(D) 105

(E) 115


Show Spoiler
Attachment:
#GREpracticequestion In the figure, what is the value of x .jpg


Since the triangle on the left side is a 3-4-5 right triangle the angle opposite the side of 5 is 90 degrees. Thus, the unlabeled angle on the left of the quadrilateral is also 90 degrees.

The triangle on the right hand side is equilateral so the angle opposite the base of 1 is 60 degrees. Thus, the unlabeled angle on the right of the quadrilateral is also 60 degrees.

A quadrilateral has 360 degrees. Therefore, we can create the following equation for the angles of the quadrilateral in the middle:

90 + x + x + 60 = 360

2x = 210

x = 105

Answer: D
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Re: In the figure, what is the value of x ? [#permalink]
07 Apr 2019, 18:58
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