SOLUTION: How can you find the sum of the interior angles of the points of a 5 point star made out of three triangles, but forming a polygon? There are no equilateral triangles and no right
Algebra ->
Polygons
-> SOLUTION: How can you find the sum of the interior angles of the points of a 5 point star made out of three triangles, but forming a polygon? There are no equilateral triangles and no right
Log On
Question 225075: How can you find the sum of the interior angles of the points of a 5 point star made out of three triangles, but forming a polygon? There are no equilateral triangles and no right angles. Answer by Edwin McCravy(20056) (Show Source):
You can put this solution on YOUR website! How can you find the sum of the interior angles of the points of a 5 point star made out of three triangles, but forming a polygon? There are no equilateral triangles and no right angles.
I'm not sure what you mean. Here's a 5-pointed star, but I don't
know how to make a 5-pointed star out of three triangles.
Did you mean this kind of 5-pointed star, also known as a pentagram?
If so, we'll extend the lines like this:
In the center is a 5-sided regular polygon (a regular
pentagon). The sum of the interior angles of a polygon
is gotten by the formula:
SUM OF INTERIOR ANGLES = (NUMBER OF SIDES - 2) * 180°
For a 5-sided polygon (pentagon) this is (5-2)*180° = 3*180°=540°
Since all 5 angles of a regular pentagon are equal, each
interior angle of the regular pentagon is ° = 108°
So I'll mark one of the 108° interior angles of the pentagon:
Its suppplement is found by subtracting 180°-108°=72°.
We'll mark it 72°:
That 72° angle is one of the base angles of an isosceles
triangle. So we'll mark the other base angle 72° also.
Now we can find the angle at the top point of the star by
adding the two equal base angles and subtracting from 180°.
72° + 72° = 144°
180° - 144° = 36°
So each point of the star is 36°.
You wanted the sum of the points interior angles of
the points. There are 5 of them, so 5 times 36° is
180°.
Edwin