Answered

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What is the sum of the measures of the interior angles of a decagon? (Note: a decagon is a polygon with 10 sides.)

A. 900 degrees
B. 1440 degrees
C. 720 degrees
D. 540 degrees

Sagot :

GinnyAnswer
To find the sum of the measures of the interior angles of a decagon (a polygon with 10 sides), you can use the following formula:

Formula:
[tex]\[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \][/tex]
where [tex]\( n \)[/tex] is the number of sides of the polygon.

For a decagon:
1. Substitute [tex]\( n = 10 \)[/tex] into the formula:
[tex]\[ \text{Sum of interior angles} = (10 - 2) \times 180^\circ \][/tex]

2. Simplify the expression inside the parentheses:
[tex]\[ 10 - 2 = 8 \][/tex]

3. Multiply the result by 180 degrees:
[tex]\[ 8 \times 180^\circ = 1440^\circ \][/tex]

Thus, the sum of the measures of the interior angles of a decagon is [tex]\( \boldsymbol{1440^\circ} \)[/tex].

So, the correct answer is:
1440 degrees.
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