Seven points are evenly spaced out on a circle and connected as shown below to form a 7-pointed star. What is the sum of the angle measurements of the seven tips of the star, in degrees? One such angle is marked as a below.

waffles
Oct 14, 2017

#2**+2 **

This is what I am imagining that you mean:

The answer is aprroximately (maybe exactly) 540 degrees

Melody
Oct 16, 2017

#6**+3 **

Looking at my picure I just thought of a much better way to do this :

I can see that the dark green arc is 3/7 of the circle.

So the angle at the centre that issubtend by this arc must be \(\frac{3}{7}*360=\frac{3*360}{7}\)

Now a very commonly used circle property is that the angle at the centre subtended by an arc is twice the angle at the circumference subtended by the same arc.

so the angle at the circumference, which is one of the points of the star must be \(\dfrac{1}{2}*\dfrac{3*360}{7}=\dfrac{3*360}{2*7}\)

So the angle sum of all points of the star is \(7*\dfrac{3*360}{2*7}=\dfrac{3*360}{2}=3*180=540^\circ\)

Melody
Oct 17, 2017