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

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 4

What is the measure of each exterior angle of a regular octagon?

Accepted Answer

For a regular octagon, number of sides $n = 8$. Each exterior angle = $\frac{360^\circ}{n} = \frac{360^\circ}{8} = 45^\circ$.

Question 5

The adjacent angles of a parallelogram are always:

Accepted Answer

In a parallelogram, adjacent angles are consecutive interior angles between parallel lines, so their sum is $180^\circ$ (supplementary).

Understanding Quadrilaterals