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In the figure, what is the value of y ?

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In the figure, what is the value of y ?  [#permalink]

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New post 21 Jun 2017, 01:52
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A
B
C
D
E

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  5% (low)

Question Stats:

90% (00:58) correct 10% (01:20) wrong based on 65 sessions

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Re: In the figure, what is the value of y ?  [#permalink]

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New post 21 Jun 2017, 01:58
Bunuel wrote:
Image
In the figure, what is the value of y ?

(A) 7.5
(B) 15
(C) 30
(D) 40
(E) 45

Attachment:
2017-06-21_1251.png


From the diagram, \(y + 30 = (y + 15) + (y - 15) = y + 15 + y - 15\)

\(y + 30 = 2y\)

\(2y - y = 30\)

\(y = 30\). Answer (C) ...
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Re: In the figure, what is the value of y ?  [#permalink]

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New post 21 Jun 2017, 02:34
Extended outside Angle of a triangle is equal to sum of opposite two angles

(y-15) + (y+15) = y+30

2y = y+30

y = 30
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Re: In the figure, what is the value of y ?  [#permalink]

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New post 22 Jun 2017, 02:56
Bunuel wrote:
Image
In the figure, what is the value of y ?

(A) 7.5
(B) 15
(C) 30
(D) 40
(E) 45

Attachment:
2017-06-21_1251.png


In a triangle, Exterior angle = Sum of interior angles
y + 30 = (y - 15) + (y + 15)
-> y = 30

Answer C
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Re: In the figure, what is the value of y ?  [#permalink]

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New post 22 Jun 2017, 08:35
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Bunuel wrote:
Image
In the figure, what is the value of y ?

(A) 7.5
(B) 15
(C) 30
(D) 40
(E) 45

Attachment:
2017-06-21_1251.png


\(( y + 30) + a = 180\)

Or, \(y + a = 150\)

Or, \(a = 150 - y\)

Now, we have -

\(( 150 - y ) + ( y - 15 ) + ( y + 15 ) = 180\)

Or, \(150 + y = 180\)

Or, \(y = 30\)

So, Answer must be (C) 30
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Re: In the figure, what is the value of y ?  [#permalink]

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New post 22 Jun 2017, 10:50
From the figure, we can deduce that
the third angle in the triangles is 180 - (y+30) = 150 - y

Sum of three angles in a triangle is 180 Degree
150 - y + y - 15 + y + 15 = 180
y + 150 = 180
y = 30(Option C)
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Re: In the figure, what is the value of y ?  [#permalink]

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New post 01 Aug 2018, 16:38
Bunuel wrote:
Image
In the figure, what is the value of y ?

(A) 7.5
(B) 15
(C) 30
(D) 40
(E) 45

Attachment:
2017-06-21_1251.png


Since an exterior angle of the triangle is equal to the sum of the two remote interior angles, we have:

y + 30 = y - 15 + y + 15

y + 30 = 2y

30 = y

Answer: C
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Re: In the figure, what is the value of y ? &nbs [#permalink] 01 Aug 2018, 16:38
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