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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°.
How many sides does a regular polygon have if each exterior angles measure is 20 degrees?
18 sides. The sum of all the exterior angles equals 360°, for any polygon. See related link.
How is the number of sides related to the sum of the interior angles of a polygon?
Because; (number of sides-2)*180 = sum of interior angles
Do the interior angle of a pentagon have to be the same measurement of the perimeter?
The angles of a polygon are not directly related to the measurement of the perimeter. If you measure a perimeter of a pentagon in inches and then again in centimetres, the measurement number will change but the pentagon will remain the same.
What is circumscribed area and inscribed area of regular polygon?
circumscribed means the polygon is drawn around a circle, and inscribed means the polygon is drawn inside the circle. See related links below for polygon circumscribed about a circle and polygon inscribed in a circle.
What is the measure of an interior angle of a regular polygon with 6 sides?
120See related link below for interior angles of various polygons.
How is the measure of each interior angle related to the number of sides in a polygon?
It is not. The sum of all the interior angles is related to the number of sides but, unless the polygon is regular, each interior angles can have any value in the range (0, 360) degrees - the traingle being an exception where the maximum angle must be less than 180 degrees. There is nothing in the question that suggests that the polygon is regular and since only a minority of polygons are regular, you may not assume that it is a regular polygon.
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 sum of the interior angles of a regular polygon if each exterior angle mesaures 90?
Looking at the related link, you will see that an exterior angle of 90° will result in an interior angle of 90°. Since it's regular, and all the angles are 90°, the only possibility is a square. So the sum of interior angles is 360°
How many sides does a regular polygon have if each exterior angles measure is 20 degrees?
18 sides. The sum of all the exterior angles equals 360°, for any polygon. See related link.
How is the number of sides related to the sum of the interior angles of a polygon?
Because; (number of sides-2)*180 = sum of interior angles
How is the number of sides related to the sum of the angles in a polygon?
The sum of all the interior angles of a polygon with n sides is (n-2)*180 degrees.
How many degree angle does regular hexagon has?
For any regular polygon, the sum of the exterior angles = 360°The interior angle = 180° - (exterior angle).So, interior angle (of a vertex) = 180° - (360° / N)Where N is the number of vertices (which is also the number of sides).For a hexagon, Interior angle = 180° - (360° / 6) = 180° - 60° = 120°See the related link at mathopenref.com
Do the interior angle of a pentagon have to be the same measurement of the perimeter?
The angles of a polygon are not directly related to the measurement of the perimeter. If you measure a perimeter of a pentagon in inches and then again in centimetres, the measurement number will change but the pentagon will remain the same.
What is the total angles interior and exterior of a ten sided polygon?
A polygon with N sides has a total of (N-2)*180° for interior. So for N=10, that's 1440° total interior. For exterior, it depends on the definition. It could be 360° or 2160°. See related links.
What is the sum of the interior angle of a sixteen sided polygon?
For an N-sided polygon, the sum of the interior angles is: N*(180° - 360°/N) or just N*180° - 360°. See related link. So for N=16, the sum is 2520°
What is circumscribed area and inscribed area of regular polygon?
circumscribed means the polygon is drawn around a circle, and inscribed means the polygon is drawn inside the circle. See related links below for polygon circumscribed about a circle and polygon inscribed in a circle.
