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1. Define Polygon, Regular Polygon, Concave Polygon, and Convex Polygon.

2. Explain interior and exterior angle properties.

3. Each exterior angle of a regular polygon with [tex]\(n\)[/tex] sides is equal to ______.

4. The ratio of the exterior angle to the interior angle of a regular polygon is 1:4. What will be the number of sides of the polygon?

5. What is the measure of each exterior angle of a regular pentagon?

6. A mason has made a concrete slab. He needs it to be rectangular. In what different ways can he make sure that it is rectangular?

7. A square is defined as a rectangle with all sides equal. Can we define it as a rhombus with equal angles? Explore this idea.



Answer :

GinnyAnswer

Final answer:

The detailed answer covers definitions of polygons, their properties, angle characteristics, and explores the concepts of regular polygons, exterior angles, and rectangular shapes.


Explanation:

Polygon: a plane figure with multiple angles and sides.

Regular Polygon: a polygon with equal sides and angles like an equilateral triangle or a square.

Concave Polygon: a polygon with at least one interior angle greater than 180 degrees.

Convex Polygon: a polygon with all interior angles less than 180 degrees.

Interior angle properties: Sum of interior angles in a polygon = (n-2) * 180 degrees where n is the number of sides.

Exterior angle properties: Sum of exterior angles in any polygon is always 360 degrees.

Ratio of exterior to interior angle: In a regular polygon, each exterior angle = 360/n degrees where n is the number of sides. Given a ratio of 1:4, the polygon must have 5 sides (Pentagon).

Measure of each exterior angle of a regular pentagon: Each exterior angle of a regular pentagon = 360/5 = 72 degrees.

Making a rectangular slab in different ways: The mason can ensure the slab is rectangular by measuring the diagonals; if they are equal, it's a rectangle. Alternatively, by ensuring all angles are right angles or opposite sides are parallel, the slab can be rectangular.

Square defined as a rhombus: A square can be defined as a rhombus since it has equal angles but differs in that all sides must be equal for a square, not just opposite sides.


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