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How many sides does an equiangular polygon have if the measure of an angle of the polygon exceeds four times the measure of one of it's exterior angles by 30?
Interior angle + Exterior angle = 180
So Interior angle = 180 - Exterior angle
Interior angle = 4*Exterior angle + 30
Substitute for Interior angle: 180 - Exterior angle = 4*Exterior angle + 30
Collect like terms: 150 = 5*Exterior angle
Divide by 5: Exterior angle = 30 deg
Therefore number of sides = 360/30 = 12
What else can I help you with?
Define equilateral and equiangular polygon?
An equilateral polygon is a polygon whose sides are all of the same measure. An equiangular polygon is a polygon whose angles are all of the same measure. A triangle is the only polygon where these two are effectively one and the same.. But it does not apply to polygons of 4 or more sides. A square and rhombus are equilateral but a rhombus is not equiangular. A square and rectangle are equiangular but a rectangle is not equilateral. This can be extended to all polygons with more than 4 sides but it is more difficult because they do not have distinctive names.
What is an equilateral polygon that is not a regular polygon?
A rhombus has four sides of equal lengths. So it is an equilateral polygon. But it is not an equiangular. It's angles are not equal in measure.
Why is an equilateral polygon not necessarily a regular polygon?
A regular polygon must be equiangular as well as equilateral. A rhombus is an example of a polygon that is equilateral but not equiangular.
What is the measure of an exterior angle in a 12 sided polygon?
Providing that it is a regular 12 sided polygon then each exterior angle measures 30 degrees
What is convex equilateral equiangular polygon called?
A regular polygon.
How do you work out the exterior angle?
Measure it. There is no formula for an exterior angle unless you have a regular (or equiangular) polygon. And there is no evidence to suggest that that is the case.
If a polygon is equiangular then is?
All the angle have the same measure.
What happens if the number of sides of an equiangular polygon is doubled?
The interior and exterior angles would change.
An equilateral hexagon that is not equiangular?
if the measure of each interior angle of a polygon is 150 degrees how amny sides does it have?
What is the largest exterior angle that any regular polygon can have?
The largest exterior angle measure is 120o. It is the exterior measure of an equilateral triangle (which is a regular polygon).
Define equilateral and equiangular polygon?
An equilateral polygon is a polygon whose sides are all of the same measure. An equiangular polygon is a polygon whose angles are all of the same measure. A triangle is the only polygon where these two are effectively one and the same.. But it does not apply to polygons of 4 or more sides. A square and rhombus are equilateral but a rhombus is not equiangular. A square and rectangle are equiangular but a rectangle is not equilateral. This can be extended to all polygons with more than 4 sides but it is more difficult because they do not have distinctive names.
What is the equiangular polygon conjecture?
Equiangular Polygon Conjecture - You can find the measure of each interior angle of an equiangular n-gon by using either of these formulas:1.) 180 (n-2) divided by n2.) 180 - (360 / n)
Is a regular polygon always equiangular?
Yes, a regular polygon is always equiangular.
What is a polygon with all angles being the same measure?
An equiangular polygon. NOT a regular polygon which requires that all the sides are also of the same length.
How do you find the measure of exterior angles on a polygon?
The exterior angles of any polygon add up to 360 degrees
What is an equilateral polygon that is not a regular polygon?
A rhombus has four sides of equal lengths. So it is an equilateral polygon. But it is not an equiangular. It's angles are not equal in measure.
What polygon has sides that are all the same length?
The polygon, as described in the question, is an equilateral polygon. If, in addition to this, all its angles have the same measure then the polygon is said to be regular. Polygons can be equilateral or equiangular or both (regular). The one exception is a triangle where equilateral implies (and is implied by) equiangular.
