Angles of Polygons
regular
A _____ polygon has all congruent sides and congruent angles.
polygon
A many sided figure is called a _____.
congruent
A regular polygon has _____ sides and angles.
linear pair
Along each side of polygons, together each interior and exterior angle forms a _____.
15°
Find the measure of one exterior angle in a regular 24-gon
6.32°
Find the measure of one exterior angle in a regular 57-gon
36°
Find the measure of one exterior angle in a regular decagon
51.43°
Find the measure of one exterior angle in a regular heptagon
40°
Find the measure of one exterior angle in a regular nonagon
45°
Find the measure of one exterior angle in a regular octagon
360/n
How do you find the measure of each exterior angle of a regular polygon?
(n-2)*180/n
How do you find the measure of each interior angle of a regular polygon?
360/n
How do you find the measure of the central angle of a regular polygon?
(n-2)*180
How do you find the sum of the interior angles of any convex polygon?
45°
How many degrees is each exterior angle of a regular octagon?
120°
How many degrees is each exterior angle of a regular triangle?
135°
How many degrees is each interior angle of a regular octagon?
60°
How many degrees is each interior angle of a regular triangle?
20
If the central angle of a regular polygon is 18°, how many sides does it have?
24°
If the central angle of a regular polygon is 24°, what is the measure of its exterior angle?
2°
If the central angle of a regular polygon is 2°, what is the measure of its exterior angle?
10
If the central angle of a regular polygon is 36°, how many sides does it have?
9
If the central angle of a regular polygon is 40°, how many sides does it have?
8
If the central angle of a regular polygon is 45°, how many sides does it have?
5
If the central angle of a regular polygon is 72°, how many sides does it have?
90°
If the central angle of a regular polygon is 90°, what is the measure of its exterior angle?
60°
If the exterior angle of a regular polygon is 120°, what is the measure of its interior angle?
45°
If the exterior angle of a regular polygon is 135°, what is the measure of its interior angle?
128.57°
If the exterior angle of a regular polygon is 51.43°, what is the measure of its interior angle?
number of sides
In the formula, (n-2)*180, what does "n" stand for?
supplementary
The interior angles and exterior angles of a regular polygon are _______.
360°
The sum of the exterior angles of ANY convex polygon is always _____.
always
The sum of the exterior angles of ANY polygon is _____ 360 degrees.
8
The sum of the interior angles of a convex polygon is 1080 degrees. How many sides does it have?
9
The sum of the interior angles of a convex polygon is 1260 degrees. How many sides does it have?
10
The sum of the interior angles of a convex polygon is 1440 degrees. How many sides does it have?
11
The sum of the interior angles of a convex polygon is 1620 degrees. How many sides does it have?
12
The sum of the interior angles of a convex polygon is 1800 degrees. How many sides does it have?
7
The sum of the interior angles of a convex polygon is 900 degrees. How many sides does it have?
30°
What is the central angle of a regular 12-gon?
18°
What is the central angle of a regular 20-gon?
60°
What is the central angle of a regular hexagon?
120°
What is the central angle of a regular triangle?
150°
What is the measure of one interior angle in a regular 12-gon?
154.29°
What is the measure of one interior angle in a regular 14-gon?
166.67°
What is the measure of one interior angle in a regular 27-gon?
135°
What is the measure of one interior angle in a regular octagon?
90°
What is the measure of one interior angle in a regular quadrilateral?
60°
What is the measure of one interior angle in a regular triangle?
360°
What is the sum of the exterior angles in a regular 240-gon?
360°
What is the sum of the exterior angles of a convex 100-gon?
360°
What is the sum of the exterior angles of a convex heptagon?
1440°
What is the sum of the interior angles in a convex decagon?
900°
What is the sum of the interior angles in a convex heptagon?
720°
What is the sum of the interior angles in a convex hexagon?
1260°
What is the sum of the interior angles in a convex nonagon?
1080°
What is the sum of the interior angles in a convex octagon?
540°
What is the sum of the interior angles in a convex pentagon?
1800°
What is the sum of the interior angles of 12-gon?
4140°
What is the sum of the interior angles of 25-gon?
11700°
What is the sum of the interior angles of 67-gon?
720°
What is the sum of the interior angles of a hexagon?
540°
What is the sum of the interior angles of a pentagon?
1620°
What is the sum of the interior angles of an 11-gon?
Exterior angles
_____ are formed by extending each side of a polygon in the same direction. (looks like a pinwheel)