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What is the sum of the polygons interior angles measure if the exterior angle of a regular polygon's 45 degree?
The sum of the polygon's interior angles, if the exterior angle is 45o, is 1080o
The sum of the exterior angles of a polygon is 360o, thus:
exterior_angle x number_of_sides = 360o
⇒ number_of_sides = 360o ÷ exterior_angle
⇒ number_of_sides = 360o ÷ 45o
⇒ number_of_sides = 8.
Interior and exterior angles of a polygon are supplementary, that is add up to 180o, thus:
interior_angle + exterior_angle = 180o
⇒ interior_angle = 180o - exterior_angle
⇒ interior_angle = 180o - 45o
⇒ interior_angle = 135o
Sum of the interior_angles for a regular polygon is:
sum_of_angles = number_of_sides x interior_angle
⇒ sum_of_angles = 8 x 135o
⇒ sum_of_angles = 1080o
What else can I help you with?
What is the measure of the sum of the exterior angles of regular polygons?
360 degree
What to regular polygons has a larger exterior angle?
An equilateral triangle is the only polygon in which the exterior angle is larger than the interior angle. They are equal in a square and smaller in all regular polygons with more sides,
Which regular polygon the measure of the exterior angle is twice the measure of the interior angle?
In a regular polygon, the measure of the exterior angle is related to the interior angle by the equation: exterior angle = 180° - interior angle. If the exterior angle is twice the measure of the interior angle, we can set up the equation: exterior angle = 2 × interior angle. Solving this gives us the equation: 180° - interior angle = 2 × interior angle, leading to 180° = 3 × interior angle, or interior angle = 60°. This corresponds to a regular hexagon, as it has interior angles of 120° and exterior angles of 60°.
What is the formulas to finding interior and exterior angles of regular polygons?
Interior Angles: n-2 (n is number of sides) ____ 180 Exterior angles are always 360 degrees.
What are the formulas for exterior and interior convex and regular polygons?
int- [180(n-2)] ext- [360/2]
What is the measure of each exterior angle of a regular 2x-gon?
Regular Polygons
What is the measure of the sum of the exterior angles of regular polygons?
360 degree
What to regular polygons has a larger exterior angle?
An equilateral triangle is the only polygon in which the exterior angle is larger than the interior angle. They are equal in a square and smaller in all regular polygons with more sides,
Which regular polygon the measure of the exterior angle is twice the measure of the interior angle?
In a regular polygon, the measure of the exterior angle is related to the interior angle by the equation: exterior angle = 180° - interior angle. If the exterior angle is twice the measure of the interior angle, we can set up the equation: exterior angle = 2 × interior angle. Solving this gives us the equation: 180° - interior angle = 2 × interior angle, leading to 180° = 3 × interior angle, or interior angle = 60°. This corresponds to a regular hexagon, as it has interior angles of 120° and exterior angles of 60°.
What is the formulas to finding interior and exterior angles of regular polygons?
Interior Angles: n-2 (n is number of sides) ____ 180 Exterior angles are always 360 degrees.
About Approximately how many degrees are in the measure of an interior angle of a regular eight sided polygon?
For regular polygons, all the interior angles are the same measure, while the sum of the exterior angles is always 360 for any regular polygon. Use these facts and the fact that each interior/exterior angle pair has a sum of 180 to answer this question. 360 divided by 8 = 45. So each exterior angle of the figure measures 45. 180 - 45 = 135, so each interior angle measures 135 degrees.
What are the formulas for exterior and interior convex and regular polygons?
int- [180(n-2)] ext- [360/2]
How can you get the measure of an interior angle if you have the measure of the exterior angle of a regular polygon?
It is: 180-exterior angle = interior angle because there are 180 degrees on a straight line
One exterior angle of a regular polygon measures 40 What is the sum of the polygons interior angle measures?
1260 degrees
If the measure of one interior angle of a regular polygon is 90 degrees how many sides does the polygon have?
The only regular polygon with an interior angle of 90 degrees is the square, which has four sides. Other polygons can have an interior angle of 90 degrees, but they would not be regular polygons.
Why does all regular polygons of the same number of sides are similar to each other?
Because their interior and exterior angles are the same measurements.
What is the measure of an angle of a regular octagon?
An interior angle of a regular octagon is 45 degrees. The exterior angles measure 315 degrees.
