146k views
0 votes
NO LINKS!! URGENT HELP PLEASE!!!

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.

User TuteC
by
7.9k points

2 Answers

7 votes

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).


\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}

♥️
\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}

User Alexander Schranz
by
8.5k points
4 votes

Answer:

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.

User Mcklayin
by
7.5k points