Download Polygon Problems

Geometry Polygon Practice
Name:________________________
Directions: Show all work
1. Find the measure of ONE interior angle in a 6. In a pentagon which is convex, two angles
regular decagon.
measure 150° each. The other angles are all
equal. Find the measure of one.
2. A hexagon that is regular has sides of
length 14 cm. What is its perimeter?
7. Find the sum of the interior angles in a
convex nonagon.
3. Find the measure of one exterior angle of a
regular octagon.
8. A certain regular polygon has an exterior
angle measuring just 4°. How many sides
does this polygon have?
4. A quadrilateral has two angles measuring
108° each and one measuring 64°. Find the
measure of the fourth angle and its adjacent
exterior angle. (It is convex)
9. Find the sum of the exterior angles, one at
each vertex, in a convex dodecagon.
5. A convex polygon has an interior angle
sum of 9360°. How many sides does it have,
AND, what is the measure of one exterior
angle?
10. A convex polygon has an interior angle
sum of 16, 920°. How many sides does it
have?
11. A convex hexagon has two interior angles
of 110°. All the other interior angles are
equal. Find all angles.
16. If a regular polygon has one exterior angle
measuring 20°, how many sides does it have?
12. Find the measure of ONE exterior angle of
a regular 72-gon.
17. Four angles of a pentagon measure 80°,
90°, 100°, and 110°. Find the fifth interior
angle.
13. If a regular polygon has one interior angle
measuring 162°, how many sides does it have?
18. Find the measure of ONE interior angle of
a regular 15-gon.
14. A regular heptagon has a perimeter 91
inches. What is the length of one side?
19. Find the sum of the exterior angles, one at
each vertex, of a convex nonagon.
15. Find the sum of the interior angles of a
convex 40-gon.
20. The sum of the measures of four exterior
angles of a convex pentagon is 297°. Find the
measure of the fifth exterior angles and its
adjacent interior angle.