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

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.

A regular octagon is a polygon with 8 equal sides and 8 equal interior angles. Each interior angle of a regular octagon measures $135^\circ$.

Here's how to draw a regular octagon using a compass and ruler (inscribing it in a circle):

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, 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.

(Since I cannot physically draw, this description outlines the steps for construction.)