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

Question

https://gmatclub.com/forum/download/file.php?id=47599 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 2019-04-26_1741.png

m1033512 · Accepted Answer

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

Posted from my mobile device

BrentGMATPrepNow · Answer

Since we're not given an information about the quadrilateral, the shape COULD be a square. 
 https://i.imgur.com/8EFGTGS.png

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

Archit3110 · Answer

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

Probus · Answer

Refer to figure

We know that A+B+C= 180 Similarly, we have D+E+F=180, G+H+I=180,J+K+L=180 ( SUM OF ANGLES IN A STRAIGHT LINE)

SO ADDING ALL WE HAVE 
A+B+C+D+E+F+G+H+I+J+K+L=180*4 = 720 ----------(1)

In quad B+E+H+K= 360 (SUM OF ANGLES IN A QUAD ) --------(2)

(1)-(2)= A+C+D+F++G+I+J+L= 720-360 = 360

cbrady4 · Answer

Isn't the simplest way to solve a problem like this (n-2)*180. Where n is the number of sides? Just want to make sure my logic is correct for this type of problem.

dcummins · Answer

Firstly, a straight line is drawn at each verticie.
Next, each of those blue dots in my diagram is equal to each other since they are vertically opposite.

Thus, 180 - (2*blue dot)= x

Notice that this must be true at each vertex, since the same relationship among the blue dots, x and the straight line exists.

We can find x from the sum of interior angles of a polygon formula:

180*(n-2) where n= # sides
180(4-2) = 180*2 = 360

Thus x = 360/4 = 90

Straight line - x = 2 blue dots (each vertex), so 180-90=2 blue dots
blue dots = 90
Thus 90*4 = 360

gmatway · Answer

lets resolve it by using logic and concepts.

we know sum on interior angles in a polygon = (n-2)*180
so here the sum of interior angles ABCD is 360 degrees.
now mark the dots of one angle as X so x+x =2x and one corner can be written as 2x+angle A=180 degrees

we have such 8x . so we can write the total as sum of all x (exterior) angles +sum of interior angles = 180degree*5 as there are 5 corners 
so we get 8x+360 =180*5 we get 8x =360degree which is our ans (sum of all exterior angles).

CrackverbalGMAT · Answer

This is a question on the concept of Polygons, specifically related to the interior angles of a polygon.

The sum of the interior angles of a ‘n’ sided polygon is given by (n-2) * 180 degrees.

The sum of all the angles on one side of a straight line is always equal to 180 degrees.

The figure shown in the diagram is a 4-sided polygon i.e. a quadrilateral. Therefore, the sum of the interior angles of the quadrilateral = (4-2) * 180 = 360 degrees.

If we denote the angles as p, q, r and s as shown in the figure below, we can say that, at every vertex, the marked angles and one of the above angles will add up to 180 degrees.

Attachment:

23rd Aug 2019 - Reply 2.JPG [ 43.05 KiB | Viewed 14818 times ]

This means that the sum of all angles at each vertex = 180 * 4 = 720 degrees. Of this, 360 degrees is the sum of p, q, r and s.
Therefore, the sum of the marked angles should be equal to 720 – 360 = 360 degrees.

The correct answer option is B.

Hope this helps!

GMATinsight · Answer

It's a pretty fine question to start the concept fo polygon hence I have discussed sum of angles for any polygon with n sides.

Check video solution as below

https://www.youtube.com/watch?v=CtvUyIjQ8do

Varunsawhney8 · Answer

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
We know sum of angles in quad=360
Hence 
720-360=360

MHIKER · Answer

Sum of angles of Quadrilateral =  180(n-2)=360

There are four straight line and angles of the straight lines  180*4 = 720

So the sum of the marked angles =  720-360 = 360

The answer is B.

Basshead · Answer

(n-2) * 180 degrees

2 * 180 = 360

180 * 4 = 720

720 - 360 = 360

Answer is B.

ramlala · Answer

Sum of angles inside quadrilateral = 360
There are four lines = Total sum of 4 lines (angles) = 180 * 4 = 720

Marked angles are the differance between both.
Answer is 720 - 360 =  360 = B

bumpbot · Answer

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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

Prep Toolkit

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