Polygons. Sums of interior and exterior angles
Answers are for parents and teachers.
1
How many diagonals does a convex 14-gon have in all?
77
2
The interior angles of a convex polygon add up to 2160°. How many sides does it have?
14
3
An interior angle of a regular polygon is 160°. How many sides does it have?
18
4
Four angles of a pentagon are 100°, 110°, 120° and 90°. How many degrees is the fifth angle?
120
5
Into how many triangles do the diagonals from one vertex cut a convex n-gon? Explain.
Into n − 2 triangles: no diagonal goes to the vertex itself or to its two neighbours, so n − 3 diagonals make n − 2 triangles.