Question

The interior angles of a polygon equal 360°. How many sides does this polygon have?

Answer 1

A 3
B 4
C 6

Answer 2

The sum of the interior angles of an n-sided polygon is \[(n-2)*180^\circ\]

Answer 3

Solve for n

S = 180(n-2)

360 = 180(n-2)

Answer 4

For a triangle, we have \(n=3\), so the sum of the interior angles of a triangle is \((3-2)*180^\circ = 180^\circ\) and I'm sure you know that to be true, even if you are unaware of the formula.

Answer 5

then what

Answer 6

Well, as Jim said, solve \[360 = (n-2)*180\]for \(n\)

Answer 7

Or think of what regular polygon has 4 sides instead of 3, and what its angles add up to...