For a hexagon, $n = 6$. Sum = $(6 - 2) \times 180^\circ = 4 \times 180^\circ = 720^\circ$.

Question 1

What is the sum of all interior angles of a quadrilateral?

Accepted Answer

The sum of all interior angles of any quadrilateral is $360^\circ$. Formula: $(n - 2) 	imes 180^\circ = (4 - 2) 	imes 180^\circ = 360^\circ$.

Question 2

What is the sum of the measures of the exterior angles of any polygon?

Accepted Answer

The sum of the measures of the exterior angles of any convex polygon is always $360^\circ$, regardless of the number of sides.

Question 3

The sum of the interior angles of a polygon with $n$ sides is given by which formula?

Accepted Answer

The formula to find the sum of interior angles of an $n$-sided polygon is $(n - 2) 	imes 180^\circ$.

Question 4

How many diagonals does a pentagon have?

Accepted Answer

Number of diagonals = $\frac{n(n - 3)}{2}$. For a pentagon ($n = 5$), $\frac{5(5 - 3)}{2} = \frac{5 	imes 2}{2} = 5$.

Question 5

What is the sum of the interior angles of a hexagon?

Accepted Answer

For a hexagon, $n = 6$. Sum = $(6 - 2) 	imes 180^\circ = 4 	imes 180^\circ = 720^\circ$.

Understanding Quadrilaterals