Question

Find the measure of each interior angle of a regular decagon . ( Hint: Decagon-
10-sided polygon)

Answer 1

Answer:144°

Step-by-step explanation:

Let I be the measure of each interior angle.

Let n be the total no. Of sides.

So, n=10

Thus by the formula,

I=((n-2)*180°)/n

=(10-2)*180°)/10

=(8*180°)/10

=1440°/10

=144°

Answer 2

The measure of each interior angle of a regular decagon is 144°

Given :

A polygon with 10 sides

To find :

The measure of each interior angle

Formula :

The sum of interior angles of a polygon with n sides = ( n - 2 ) × 180°

Solution :

Step 1 of 3 :

Write down the number of sides

Here the given polygon is regular decagon

Decagon is a 10 sided polygon

So the polygon has 10 sides

Step 2 of 3 :

Find sum of interior angles of a polygon

Number of sides = n = 10

The sum of interior angles of the polygon

= ( 10 - 2 ) × 180°

= 8 × 180°

= 1440°

Step 3 of 3 :

Measure each interior angle

Number of sides = n = 10

The sum of interior angles of the polygon = 1440°

The measure of each interior angle

$\displaystyle \sf{ = \frac{ {1440}^{ \circ}}{10} }$

$\sf = {144}^{ \circ}$

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