Question

find the sum of interior angle of pentagon, hexagon, octagon ​

Answer 1

I hope this is helpfull to you..To find the sum of interior angles of a polygon, multiply the number of triangles in the polygon by 180°. is the number of sides. All the interior angles in a regular polygon are equal. The formula for calculating the size of an interior angle is: interior angle of a polygon = sum of interior angles ÷ number of sides.

(in pentagon .. 360/5=72degree each angle.

in hexagon..360/6=60degree each angle.

in octagon..360/8=45degree each angle)

Answer 2

Answer:

To Find:-

• Sum of interior angles of:

1. Pentagon
2. Hexagon
3. Octagon

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We know, Sum of interior angles of a polygon (Let the sides be n):-

$\boxed{\large\tt{(n-2) \times {180}^{\circ}}}$

(Note:

If we divide the formula by the sides, the measure of one angle will be the outcome. The formula in the case will be:-

$\boxed{\large\sf{\frac {(n-2) \times {180}^{\circ}}{n}}}$

where, n is the number of side. )

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$\large\text{Pentagon:-}$

No. of sides in it = 5

Hence,

$\tt{(5-2) \times {180}^{\circ}}$

(Formation of Equation as per the formulae)

$\tt{=3 \times {180}^{\circ}}$

(Subtracted 2 from 5 and the result is 3)

$\text\green{={540}^{\circ}}$

$\tt{(Answer)}$

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$\large\text{Hexagon:-}$

No. of side in a Hexagon = 6

Henceforth,

$\tt{(6-2) \times {180}^{\circ}}$

(Formation of Equation as per the formulae)

$\tt{=4 \times {180}^{\circ}}$

(Subtracted 2 from 6 and the result is 4)

$\text\green{={720}^{\circ}}$

$\tt{(Answer)}$

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$\large\text{Octagon:-}$

No. of sides in an Octagon = 8

Hence,

$\tt{(8-2) \times {180}^{\circ}}$

(Formation of Equation as per the formulae)

$\tt{=6 \times {180}^{\circ}}$

(Subtracted 2 from 8 and the result is 6)

$\text\green{={1080}^{\circ}}$

$\tt{(Answer)}$

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REQUIRED ANSWER:-

• Sum of interior angles of a:

1. Pentagon : $\boxed{\tt{{540}^{\circ}}}$
2. Hexagon : $\boxed{\tt{{720}^{\circ}}}$
3. Octagon : $\boxed{\tt{{1080}^{\circ}}}$