Angles and Polygons

1.  What is the sum of the measures of the angles of a triangle?  What is the sum of the angles of a triangle measured in degrees?

2.  What is the sum of the interior angles of a convex 8-gon?

3.  What is the sum of the interior angles of a convex n-gon?

4.  Is it possible to have a quadilateral with all interior angles being acute angles?  Explain!

5.  If the sum of the interior angles of a convex polygon is 1440º, how many sides does the polygon have?

6.  What is a regular polygon?

7.  What is the measure of each interior angle of a regular convex 8-gon?

8.  What is the measure of each interior angle of a regular convex n-gon?

9.  What is the measure of each interior angle in a regular convex 18-gon?

10.  If the measure of each interior angle of a regular convex n-gon is 171º, how many sides does the polygon have?

11.  An exterior angle of a polygon is formed when one extends, at a vertex, one of the sides coming into that vertex.  The angle formed by this extension and the other side at that vertex is an exterior angle.  See diagram below.  What is the sum of the exterior angles, one at each vertex, in a convex quadilateral?

12.  What is the sum of the measures of the exterior angles, one at each vertex, of a convex hexagon?

13.  What is the sum of the measure of the exterior angles, one at each vertex, of a convex n-gon?

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