Hexagon Sum = (4)cdot 180^circ =720^circ All regular polygons are equiangular, therefore, we can find the measure o angle by: One interior angle of a regular polygon=((n-2)cdot 180^circ )/(n) For a hexagon: One interior angle=(720^circ )/(6)=120^circ Note: The previous information could also be used to find the number regular polygon given the measure of one interior angle. Example: How many sides does a regular polygon have if one measures 157.5^circ From above: 157.5=((n-2)cdot 180)/(n) OR 157.5n=(n- What is the value of n? PRACTICE... Show all work required to complete each of the following 1) What is another name for a regular quadrilateral? 2) Find the sum of the measures of the interior angles of a convex r 3) What is the measure of each interior angle of a regular pentago

Question

Hexagon Sum = (4)cdot 180^circ =720^circ All regular polygons are equiangular, therefore, we can find the measure o angle by: One interior angle of a regular polygon=((n-2)cdot 180^circ )/(n) For a hexagon: One interior angle=(720^circ )/(6)=120^circ Note: The previous information could also be used to find the number regular polygon given the measure of one interior angle. Example: How many sides does a regular polygon have if one measures 157.5^circ From above: 157.5=((n-2)cdot 180)/(n) OR 157.5n=(n- What is the value of n? PRACTICE... Show all work required to complete each of the following 1) What is another name for a regular quadrilateral? 2) Find the sum of the measures of the interior angles of a convex r 3) What is the measure of each interior angle of a regular pentago

Answer 1

1) Another name for a regular quadrilateral is a square.2) To find the sum of the measures of the interior angles of a convex regular polygon, we can use the formula:Sum of interior angles = (n-2) * 180°where n is the number of sides of the polygon.For a regular quadrilateral (square), n = 4.Sum of interior angles = (4-2) * 180° = 2 * 180° = 360°3) To find the measure of each interior angle of a regular pentagon, we can use the formula:Interior angle = (n-2) * 180° / nwhere n is the number of sides of the polygon.For a regular pentagon, n = 5.Interior angle = (5-2) * 180° / = 3 * 180° / 5 = 108°Therefore, the measure of each interior angle of a regular pentagon is 108°.

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