Problem Solving

can anybody please explain me question number 10 from page 21 of OG13

can anybody please explain me question number 10 from page 21 of OG13[/quote]

Within the STAR you'll see a pentagon(Polygon having 5 sides)--->{in red color, fig. 1}
For any polygon, the sum of all the interior angles = 180(n-2), where n is the number of sides of the polygon.
Lets call the 5 angles of pentagon a, b, c, d & e
Now, sum of interior angles of pentagon = 180(5-2)=540
therefore, a+b+c+d+e=540
Take a look at the figure, we can find 5 triangles, with which we can form following equations:
a+x+z=180
b+v+y=180
c+x+w=180
d+v+z=180
e+y+w=180
(sum of interior angles of triangle=180)
Now add them all, we have a+b+c+d+e+2v+2w+2x+2y+2z=180*5
2v+2w+2x+2y+2z=900-540------->(a+b+c+d+e=540)
2v+2w+2x+2y+2z=360
v+w+x+y+z=180

thank you so much....