Question

pls answer correct. its very very very important.

Answer 1

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In the following figure, the center section of the star is a pentagon.

The sum of the interior angles of any polygon is 180(n−2), where n is the number of sides. Thus, a+b+c+d+e=180(5−2)=180(3)=540.

Each of the interior angles of the pentagon defines a triangle with two of the angles at the points of the star. This gives the following five equations:

a+x+z=180

b+v+y=180

c+x+w=180

d+v+z=180

e+y+w=180

Summing these 5 equations gives:

a+b+c+d+e+2v+2x+2y+2z+2w=900.

Substituting 540 for a+b+c+d+e gives: 540+2v+2x+2y+2z+2w=900.

From this:

2v+2x+2y+2z+2w=360 subtract 540 from both sides

2(v+x+y+z+w)=360 factor out 2 on the left side

v+x+y+z+w=180 divide both sides by 2

The correct answer is C.

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Answer 2

Step-by-step explanation:

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