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n is number of sides. Sum of interior angles is 180n - 360, so 180n = 2880 + 360, ie 3240 and n = 3240/180 ie 18.

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Q: How many sides does a convex ploygon have if the measures of its interior angles have a sum of 2880?
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How many angles are larger than a right angle on a pentagon?

Each interior angle of a regular pentagon is 108 degrees ie all five of them are larger than a right angle. If the pentagon is convex, at least four of the angles must be greater than 90 degrees.


Why is the sum of the exterior angle measures of a convex polygon is always 360 degrees?

It is because if you shorten the sides yet keep the angles the same size, the shape will eventually become a pinwheel and thus, because a circle is always 360 degrees, the outer angles will always be 360 degrees.


What is the measure of one interior angle of a regular convex 31gon?

The easiest way to calculate this is to use the facts thatthe sum of the interior and exterior angles is 180o; andthe sum of the exterior angles of any polygon is 360o.For a regular polygon, each exterior angle will be 360o divided by the number of sides. The interior angle is then 180o - the exterior angle.For a 31-gon:exterior_angle = 360° ÷ 31= 1119/31o⇒ interior_angle = 180° - 1119/31o= 16812/31°≈ 168.39oUse the Interior Angle Formula directlyThe sum of interior angles for a polygon of n sides is (n-2) x 180° and individual angles for a regular polygon will be (n-2) 180°/nPlugging in the value n=31, we have one angle = 29(180)/31 = 168.39°


A regular polygon is defined to be a convex polygon with all sides and all angles?

congruent; congruent


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