MathScore EduFighter is one of the best math games on the Internet today. You can start playing for free!

## Polygon Angles - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

See some of our other supported math practice problems.

### Complexity=1, Mode=sum

Solve.

 1.   What is the sum of the interior angles of a quadrilateral?    ° 2.   What is the sum of the exterior angles of an octagon?    °

### Complexity=2, Mode=sum

Solve.

 1.   How many sides does a polygon have if the sum of its interior angles is 1260°? 2.   How many sides does a polygon have if the sum of its interior angles is 180°?

### Complexity=1

Solve.

 1.   What is the measurement of an interior angle of a regular nonagon?    ° 2.   What is the measurement of an exterior angle of a regular triangle?    °

### Complexity=2

Solve.

 1.   An exterior angle of a regular polygon measures 36°. How many sides does the polygon have? 2.   An interior angle of a regular polygon measures 60°. How many sides does the polygon have?

### Complexity=1, Mode=sum

Solve.

1What is the sum of the interior angles
°
Solution
To find the sum of the interior angles of a polygon, use the formula
180 (n - 2) where n is the number of sides.

Sum of the interior angles of a quadrilateral = 180 (4 - 2) = 360 degrees
2What is the sum of the exterior angles
of an octagon?
°
Solution
The sum of the exterior angles of a polygon is always 360°.

### Complexity=2, Mode=sum

Solve.

1How many sides does a polygon have if
the sum of its interior angles is
1260°?

Solution
To find the sum of the interior angles of a polygon, use the formula
180 (n - 2) where n is the number of sides.

Apply the formula to solve for n.
 180 (n - 2) = 1260 n - 2 = 7 n = 9
2How many sides does a polygon have if
the sum of its interior angles is
180°?

Solution
To find the sum of the interior angles of a polygon, use the formula
180 (n - 2) where n is the number of sides.

Apply the formula to solve for n.
 180 (n - 2) = 180 n - 2 = 1 n = 3

### Complexity=1

Solve.

1What is the measurement of an interior
angle of a regular nonagon?
°
Solution
To find the measure of each interior angle of a regular polygon, use the formula
 180 (n - 2) where n is the number of sides. n

 180 (9 - 2) = 140 9
2What is the measurement of an exterior
angle of a regular triangle?
°
Solution
To find the measure of each interior angle of a regular polygon, use the formula
 360 where n is the number of sides. n

 360 = 120 3

### Complexity=2

Solve.

1An exterior angle of a regular polygon
measures 36°. How many sides does
the polygon have?

Solution
To find the measure of each interior angle of a regular polygon, use the formula
 360 where n is the number of sides. n

Apply the formula to solve for n.
 360 = 36 n 360 = 36n 360 = n 36 n = 10
2An interior angle of a regular polygon
measures 60°. How many sides does
the polygon have?

Solution
To find the measure of each interior angle of a regular polygon, use the formula
 180 (n - 2) where n is the number of sides. n

Apply the formula to solve for n.
 180 (n - 2) = 60 n 180n - 360 = 60n 120n = 360 n = 3