Question

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1. Find the sum of the measures of the interior angles of the indicated polygons. (NOT MULTIPLE CHOICE)
a. heptagon

b. 13-gon

2. The sum of the measures of the interior angles of a convex polygon is 1260°. Classify the polygon by the number of sides.

Answer 1

1a. Sum of interior angles of a heptagon:

`\displaystyle \sf \text{Sum of interior angles} = (7 - 2) * 180^\circ = 900^\circ`

1b. Sum of interior angles of a 13-gon:

`\displaystyle \sf \text{Sum of interior angles} = (13 - 2) * 180^\circ = 1980^\circ`

2. Number of sides for a polygon with a sum of interior angles of 1260°:

`\displaystyle \sf (n - 2) * 180^\circ = 1260^\circ`

`\displaystyle \sf n - 2 = (1260^\circ)/(180^\circ)`

`\displaystyle \sf n - 2 = 7`

`\displaystyle \sf n = 7 + 2 = 9`

Therefore, the sum of the measures of the interior angles of a heptagon is 900°, the sum of the measures of the interior angles of a 13-gon is 1980°, and the polygon with a sum of interior angles of 1260° is a nonagon (9-gon).

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Answer 2

1. a. 900° b. 1980°

2. Nonagon

Explanation:

In order to find the interior angles of a polygon, use the formula,

Sum of interior angles = (n-2)*180°

For

a. Heptagon

no of side =7

The sum of the interior angles of a heptagon:

(7-2)*180 = 900°

b. 13-gon

no. of side =13

The sum of the interior angles of a 13-gon:
(13-2)*180 = 1980°

2.

The sum of the interior angles of a convex polygon is 1260°,

where n is the number of sides.

In this case, we have

1260 = (n-2)*180

1260/180=n-2

n-2=7

n=7+2

n=9

Therefore, the polygon has 9 sides and is classified as a nonagon.