Applying Properties of Polygons

What do the exterior angles of a triangle have a sum of?

• 180

• 360

• 90

• 45

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

• 30 degrees

• 75 degrees

• 45 degrees

• 60 degrees

What is the degree of one exterior angle of a regular decagon(10 sides)?

• 36°

• 360°

• 10°

• 72°

Find the exterior angle on a regular polygon with 10 sides...

• 36^o

• 144^o

• rooster

• 150^o

For a regular pentagon, the exterior angle is ____ than the interior angle.

• Smaller

• Greater

• Equal

• Can not be determined

Answer explanation

For n sided regular polygon Interior angle = (n-2) x 180°/n where n is the number of sides and exterior angle = 360°/n For pentagon n = 5 So, interior angle of a regular pentagon = (5-2) x 180°/5 = 3/5 x 180° = 108° And, exterior angle of a regular pentagon = 360°/5 = 72° hence the exterior angle of a regular pentagon is smaller than its interior angle.

Which should you use to solve for x?

• Find the Central Angle
  360÷n

• Find the Sum of Exterior ∠'s
  360^o

• Find the Sum of Interior ∠'s
  180(n-2)

• Find each Interior ∠
  180(n-2)÷n

How many sides(n) does a polygon have if one exterior angle is 60°

• 9 sides

• 6 sides

• 3 sides

• 12 sides

Find the measure of one exterior angle of a regular 18-gon.

• 160°

• 360°

• 20°

• 2280°

Find the interior angle if the exterior angle is 60 degrees.

• 30

• 90

• 180

• 120

What is the sum of the measures of the exterior angles of a decagon?

• 1440⁰

• 360⁰

• 144⁰

• 1800⁰