Assertion: regular polygon's angle | /r/HasProperty | supplementary
Facets:
value: to the exterior angle
type: OTHER
value: to an exterior angle
type: TRANSITIVE-OBJECT
value: necessarily
type: DEGREE
value: at any given vertex
type: LOCATION
value: in any regular polygon
type: LOCATION
value: always
type: DEGREE
Source sentences:
text: In any regular polygon, every interior angle is supplementary to every exterior angle.
text: Interior and exterior angles are supplementary angles, meaning that the sum of their measures is equal to $180^{\circ}.$
text: The external angle at each vertex of a convex regular polygon will be the same, and will be the difference between the internal angle at that vertex and one hundred and eighty degrees, since the internal and external angles of a convex polygon are always supplementary (add up to one hundred and eighty degrees).
text: Internal and external angles of a convex regular polygon are supplementary
text: We already know that an octagon has internal angles of one hundred and thirty-five degrees (135°), and since the internal and external angles of a convex polygon are supplementary (i.e. they add up to one hundred and eighty degrees) then the external angles must be forty-five degrees (45°).
text: Since you are extending a side of the polygon, that exterior angle must necessarily be supplementary to the polygon's interior angle.
text: Exterior and Interior angles are supplementary
text: At any given vertex, the interior angle is supplementary to an exterior angle.
text: The interior angle First find the exterior angle of the polygon: since the exterior and interior angles of a polygon are supplementary, they sum to 180o, so subtract the interior angle from 180o to get the exterior angle; then use the method of the exterior angle above.
text: the interior angle is supplementary to the exterior angle, as it should be, so this checks out.