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# In the figure above, what is the value of a?

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Math Expert
Joined: 02 Sep 2009
Posts: 53063
In the figure above, what is the value of a?  [#permalink]

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17 Jan 2019, 23:24
1
00:00

Difficulty:

5% (low)

Question Stats:

88% (00:43) correct 13% (00:29) wrong based on 30 sessions

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In the figure above, what is the value of a?

A 30
B 35
C 140
D 145
E 150

Attachment:

2019-01-18_1123.png [ 6.7 KiB | Viewed 316 times ]

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

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Updated on: 18 Jan 2019, 10:48
Bunuel wrote:

In the figure above, what is the value of a?

A 30
B 35
C 140
D 145
E 150

Attachment:
2019-01-18_1123.png

solve for x we get = 35
so 35+a = 180
a = 1145
IMO d
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Originally posted by Archit3110 on 18 Jan 2019, 06:01.
Last edited by Archit3110 on 18 Jan 2019, 10:48, edited 1 time in total.
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Re: In the figure above, what is the value of a?  [#permalink]

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18 Jan 2019, 09:36
Actually answer is 145, as x is 35, not 30.

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

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18 Jan 2019, 10:19
The correct answer is option D.145

If we see name the vertices (or the corners) of the triangle as A,B,C with A being the top-most corner, B being the left-most and C being the right-most corner.

Now we know that the sum of angle in a triangle must be 180 degrees.

So we have:
angle(ABC) + angle(BAC) + angle(ACB) = 180
or
x + 3x + 40 = 180
which gives
4x = 140
and x = 140/4 = 35 degrees

Now at corner B, we can see that, x + a = 180 degrees
This is because of BC being a straight line.

so from here we get, a = 180-35 = 145 degrees.
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Re: In the figure above, what is the value of a?  [#permalink]

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18 Jan 2019, 10:30
Bunuel wrote:

In the figure above, what is the value of a?

A 30
B 35
C 140
D 145
E 150

Sum of a triangle = 180
4x + 40 = 180
x = 35

< a + < x = 180 since they are present on a straight line
a = 180 - 35
a = 145

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Re: In the figure above, what is the value of a?   [#permalink] 18 Jan 2019, 10:30
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