Answered

What is the sum of the measures of the interior angles of a heptagon?

A. [tex]$900^{\circ}$[/tex]

B. [tex]$360^{\circ}$[/tex]

C. [tex][tex]$45^{\circ}$[/tex][/tex]

D. [tex]$1080^{\circ}$[/tex]

E. [tex]$1260^{\circ}$[/tex]

F. [tex][tex]$1440^{\circ}$[/tex][/tex]



Answer :

GinnyAnswer
To determine the sum of the measures of the interior angles of a heptagon, we can use the formula for finding the sum of the interior angles of any polygon:

[tex]\[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \][/tex]

where [tex]\( n \)[/tex] is the number of sides of the polygon.

Step-by-step:

1. Identify the number of sides of the polygon. A heptagon has:
[tex]\[ n = 7 \][/tex]

2. Substitute [tex]\( n = 7 \)[/tex] into the formula:
[tex]\[ \text{Sum of interior angles} = (7 - 2) \times 180^\circ \][/tex]

3. Perform the subtraction inside the parentheses:
[tex]\[ (7 - 2) = 5 \][/tex]

4. Multiply the result by 180 degrees:
[tex]\[ 5 \times 180^\circ = 900^\circ \][/tex]

Therefore, the sum of the measures of the interior angles of a heptagon is [tex]\( 900^\circ \)[/tex].

The correct answer is:
A. [tex]\( 900^\circ \)[/tex]

Answer: A

Step-by-step explanation:

Since a heptagon has 7 sides, we can use the formula (7 - 2) * 180. This equals 900, so the answer is 900