Define polygon, give examples. Find interior angle of regular hexagon. Find number of sides of polygon with interior angle sum of 1260.

Define the term polygon. Give two examples of polygons.

• Definition: A polygon is a closed two-dimensional shape made up of straight line segments connected end-to-end to form a boundary. The line segments are called sides, and the points where they meet are called vertices.
• Examples:
  • Triangle
  • Square

Find the measure of each interior angle of a regular hexagon.

A polygon has an interior angle sum of $1260^\circ$. Calculate the number of sides it has.

One angle of a regular polygon measures $150^\circ$. Find the number of sides.

Draw a regular Octagon.

(As an AI, I cannot physically draw. Below are the steps to construct a regular octagon using a compass and ruler.)

To draw a regular octagon:

1. Draw a Circle: Use a compass to draw a circle. Mark its center point.
2. Draw Perpendicular Diameters: Draw a horizontal diameter and a vertical diameter through the center of the circle. These two diameters will divide the circle into four $90^\circ$ sectors.
3. Bisect the Angles: Bisect each of the four $90^\circ$ angles. To do this, you can place the compass point on the center, open it to any convenient radius, and draw arcs that intersect the circle and the existing diameters. Then, from the intersection points on the circle, draw two more arcs that intersect each other within each $90^\circ$ sector. Draw a line from the center through this intersection point to the circumference. This will create lines that divide each $90^\circ$ angle into two $45^\circ$ angles.
4. Mark Vertices: You will now have 8 equally spaced points on the circumference of the circle where the lines intersect the circle. These points are the vertices of the regular octagon.
5. Connect the Vertices: Use a ruler to connect these 8 points consecutively with straight line segments. These segments will form the 8 equal sides of the regular octagon.