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

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

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

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.

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

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).

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.


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!

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

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

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.

(n-2) * 180 degrees

2 * 180 = 360

180 * 4 = 720

720 - 360 = 360

Answer is B.

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

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