What are the sum of the measures of the interrior angles of a convex hexagon?
What is the sum of the measures of the angles of a convex quadrilateralwill this property hold if the quadrilateral is not convex?
The sum of all angles of any polygon does not depend on what kind of polygon it is. It depends on the number of sides a polygon has. So that the sum of all angles of the given hexagon (a 6-sided polygon) is 720°, found by using the formula Sum of a polygon angle measures = 180°(n - 2), where n is the number of sides. Since this is a convex hexagon, all its interior…
It depends on what the angles are. If any of the angles have measurements greater than 180 degrees, it is concave. If all angles are less than 180 degrees, then it is concave. For example, a regular hexagon has six 120 degree angles, so it is convex. If there was a hexagon with five 90 degree angles and one 270 degree angle, it would be concave.
a polygon with 6 sides * * * * * The fact that is has six sides makes it a hexagon but that does not explain ""convex". A convex polygon is one in which none of the angles is a reflex angle. An alternative definition of convex is that a line joining any two points inside the hexagon is wholly inside the shape.
3 maximum. A hexagon has 720Â°. With 3 right angles = 270Â°, this leaves 450Â° divided over the remaining 3 (average 150Â° each). If it had 4 right angles, then there would be 360Â° to be divided between the remaining two angles. So one of the angles would have to be greater than 180Â° (making it concave, not convex). An angle at a vertex cannot equal 180Â°, because that would be a straight line, then…
It is generally accepted to count only one vertex per side when calculating the sum of exterior angles. If this is what you mean, then for every convex polygon (all angles point away from center), the sum is always 360º. However, you can also count two vertexes per side, so the sum would then be double, or 720º.