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# In the figure, what is the value of y ?

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Math Expert
Joined: 02 Sep 2009
Posts: 51073
In the figure, what is the value of y ?  [#permalink]

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21 Jun 2017, 00:52
00:00

Difficulty:

5% (low)

Question Stats:

90% (01:00) correct 10% (01:20) wrong based on 67 sessions

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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 [ 11.22 KiB | Viewed 1220 times ]

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

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21 Jun 2017, 00:58
Bunuel wrote:

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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21 Jun 2017, 01:34
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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22 Jun 2017, 01:56
Bunuel wrote:

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

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

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22 Jun 2017, 07:35
1
Bunuel wrote:

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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22 Jun 2017, 09:50
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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01 Aug 2018, 15:38
Bunuel wrote:

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

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Re: In the figure, what is the value of y ? &nbs [#permalink] 01 Aug 2018, 15:38
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