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# In the figure above, lines are drawn at the vertices of the quadrilate

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Joined: 02 Sep 2009
Posts: 55188
In the figure above, lines are drawn at the vertices of the quadrilate  [#permalink]

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26 Apr 2019, 06:43
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Difficulty:

5% (low)

Question Stats:

86% (01:08) correct 14% (01:13) wrong based on 43 sessions

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In the figure above, lines are drawn at the vertices of the quadrilateral as shown. What is the sum of the degree measures of the marked angles?

A. 450
B. 360
C. 270
D. 240
E. 180

PS15602.01
Quantitative Review 2020 NEW QUESTION

Attachment:

2019-04-26_1741.png [ 11.06 KiB | Viewed 422 times ]

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In the figure above, lines are drawn at the vertices of the quadrilate  [#permalink]

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Updated on: 26 Apr 2019, 22:04
IMO B

Sum of angles formed by 4 straight linea = 180*4= 720

sum of angles of quad = 360

so aum the angles shown in picture = 720-360 = 180

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Originally posted by m1033512 on 26 Apr 2019, 08:48.
Last edited by m1033512 on 26 Apr 2019, 22:04, edited 1 time in total.
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Re: In the figure above, lines are drawn at the vertices of the quadrilate  [#permalink]

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26 Apr 2019, 10:03
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Top Contributor
Bunuel wrote:

In the figure above, lines are drawn at the vertices of the quadrilateral as shown. What is the sum of the degree measures of the marked angles?

A. 450
B. 360
C. 270
D. 240
E. 180

Since we're not given an information about the quadrilateral, the shape COULD be a square.

Since angles on a line add to 180°, we know that a + b + 90 = 180, which means a + b = 90

Likewise, we know that c + d + 90 = 180, which means c + d = 90

Applying the same logic, we can see that e + f = 90 and g + h = 90

So, the sum of all 8 angles = a + b + c + d + e + f + g + h
= (a + b) + (c + d) + (e + f) + (g + h)
= (90) + (90) + (90) + (90)
= 360

Cheers,
Brent
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Re: In the figure above, lines are drawn at the vertices of the quadrilate  [#permalink]

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28 Apr 2019, 03:57
alternatively we can solve seeing pic
4 sides are given & for each side the line has angle 180*
since two sides are adjacent are equal so we have total 4*(180-2x)=0
solve for x = 45
so the internal angle of the quadrilateral is 180-90; 90 * and the sum of marked angles ; 90*4 ; 360*
IMO B

Bunuel wrote:

In the figure above, lines are drawn at the vertices of the quadrilateral as shown. What is the sum of the degree measures of the marked angles?

A. 450
B. 360
C. 270
D. 240
E. 180

PS15602.01
Quantitative Review 2020 NEW QUESTION

Attachment:
2019-04-26_1741.png

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Re: In the figure above, lines are drawn at the vertices of the quadrilate   [#permalink] 28 Apr 2019, 03:57
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