Question

The sum of all interior anges of a regular polyeon is 1080 What is the measure of each of
its interior anges?
(b) 1200
(c) 150
(d) 144
a) 135


With best explanation
Who gives best explanation will be mark as brainest​

Answer 1

ANSWER:

• Measure of each of the interior angle = 135

GIVEN:

• The sum of all interior angles of a regular polygon is 1080.

TO FIND:

• Measure of each of the interior angles.

EXPLANATION:

Sum of interior angles of a polygon = ( n - 2 )180°, Where n is the number of sides.

( n - 2 ) × 180° = 1080

(n - 2) = 108 / 18

(n - 2) = 6

n = 8

The given polygon is a octagon

Measure of each of the interior angle = (Sum of the interior angle) ÷ ( number of sides)

Measure of each of the interior angle = 1080 / 8

Measure of each of the interior angle = 135.

Answer 2

$\large\sf\underline{\underline{\pink{\sf Answer}}}$

☞ Your Answer is 135°

$\large\sf\underline{\underline{\red{\sf Given}}}$

✭ Sum of all the interior angles is 1080°

$\large\sf\underline{\underline{\green{\sf To \ Find}}}$

◈ Measure of the external angles

$\large\sf\underline{\underline{\blue{\sf Solution}}}$

→ So here as we have to find the measure of the interior angle

We know that the sum of interior angles is given by,

(number of sides - 2)180°

Substituting the given values,

➝ (n - 2) × 180° = 1080

➝ (n - 2) = 108/18

➝ (n - 2) = 6

➝ n = 8

The Measure of each interior Angle is given by,

(Sum of the interior angle) ÷ ( number of sides)

Substituting the values,

»» 1080/8

»» Measure of each of the interior angle = 135

Note :- Here n is the number of sides

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