Objective 49 Honors Geometry WP: Polygons

An advertising executive was using her computer to design a graphic in the shape of a convex regular polygon. If one of the exterior angles has a measure of about 51.43°, what is the name of the polygon? [A] heptagon [B] decagon [C] nonagon [D] octagon

In a rancher’s octagonal plot of land, when interior angles are put in increasing order, each differs from the next by 15°. Find the measure of the smallest interior angle of the field to the nearest tenth of a degree. [A] 810° [B] 187 5° [C] 82 5° [D] 135 0°

In a person’s heptagonal yard, when interior angles are put in decreasing order, each differs from the next by 25°. Find the measure of the largest interior angle of the field to the nearest tenth of a degree. [A] 2051° [B] 203.6° [C] 53.6° [D] 128.6°

A hog farmer has enough material for 585 meters of fence. She knows that a circle maximizes the area-to-perimeter ratio, but a circular fence is too difficult to construct. She decides to simulate a circle by building a fence in the shape of a regular polygon with as many sides as possible, but with not less than five and not more than 15 sides. If she wishes to make each side a length of an even meter, and she wishes to have no more than 3 meters left over, which regular polygon would you recommend she build, and how long would each side be? [A] 15-gon; 39 m [B] 14-gon; 42 m [C] hexagon; 98 m [D] nonagon; 65 m