Polygonal Angles
What is the sum of the interior angles of a Triangle?
180°
What do you call a five-sided polygon?
Pentagon
What is the formula for finding the sum of the interior angles of an n-sided polygon?
(n-2) * 180
What is the measure of one interior angle in a regular hexagon?
(6-2)*180/6= 120°
What is the sum of the exterior angles of any polygon?
360° (The sum of the exterior angles of any polygon is always 360°
A quadrilateral has four angles measuring 90°,85°, and 95°. What is the measure of the missing angle?
The sum of interior angles in a quadrilateral is 360°, so 360° - (90° + 85° + 95°) = 90°.
What is the difference between a convex and a concave polygon?
A convex polygon has all interior angles less than 180°; a concave polygon has at least one angle greater than 180°.
One goes in, one goes out
What is the mathematical formula used to find the number of sides of a polygon given the sum of exterior angles
n= 360/n
A polygon has an interior angle sum of 1440°. How many sides does it have?
(n-2) * 180 = 10
What is the measure of one exterior angle of a regular octagon?
360/8= 15
What is the measure of one interior angle in a regular pentagon?
108°
What is the name of a regular polygon with ten sides?
Decagon
What is the formula used to find the number of sides in a polygon given the sum of interior angles?
s=(n-2)*180 where is S is known
The interior angles of a quadrilateral measure 90°, 120°, and 110°. What is the degree of the missing angle?
Sum of quadrilateral angles = 360°. 360° - (90° + 120° + 110°) = 40°.)
A regular polygon has an exterior angle of 40°. How many sides does the polygon have?
n=360/40 = 9 sides
How many degrees are in the sum of the interior angles of an octagon?
Octagon: (8-2) times 180 = 1080°.
A polygon has all sides and angles equal. What type of polygon is this?
A regular polygon (All sides and angles are equal.)
What is the Mathematical formula used to find the number of sides in a polygon given a single exterior angle?
360/exterior angle=n
What is the interior sum of a triangle?
180 degrees
The exterior angles of a polygon sum to 360°. If one exterior angle is 24°, how many sides does the polygon have?
n=360/24 =15
A 12-Sided polygon has one missing angle. If the sum of the other 11 angles is 1600°, what is the measure of the missing angle?
For a 12-sided polygon: (12-2) \times 180 = 1800°, so missing angle is 1800° - 1600° = 180°.
What is the maximum number of obtuse angles a convex hexagon can have?
A convex hexagon can have at most three obtuse angles because their sum cannot exceed 360°
A polygon has an interior angle sum of 1980°. How many sides does it have?
(n-2)*180=1980, solving for n, we get n = 13.
Each interior angle of a regular polygon is 135°. How many sides does it have?
Each interior angle = 135°. Using (n-2)*180/n=135
We get n = 8 sides.
The total sum of all exterior angles in a N-gon?
360 degrees