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

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

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New post 26 Apr 2019, 06:43
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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


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2019-04-26_1741.png
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In the figure above, lines are drawn at the vertices of the quadrilate  [#permalink]

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New post 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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New post 26 Apr 2019, 10:03
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Bunuel wrote:
Image
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.
Image

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

Answer: B

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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New post 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:
Image
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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In the figure above, lines are drawn at the vertices of the quadrilate

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