The interior angles of an octagon are in A.P. The smallest angle is 30∘ and the common difference is 30∘.Find the sum of all the angles.

a=30∘,d=30∘Sum of interior angles=2n[2a+(n−1)d]=28[2×30∘+(8−1)30∘]=4[60∘+210∘]=4×270∘=1080∘∴ Sum of interior angles=1080∘

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The interior angles of an octagon are in A.P. The smallest ang

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The interior angles of an octagon are in A.P. The smallest angle is $30^{\circ}$ and the common difference is $30^{\circ}$ .Find the sum of all the angles.

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James Discussed

The interior angles of an octagon are in A.P. The smallest angle is

30^{\circ}

and the common difference is

30^{\circ}

.Find the sum of all the angles.

8 mins ago

Discuss this question LIVE

8 mins ago

a = 30^{\circ}, d = 30^{\circ}

Sum of interior angles

= \frac{n}{2} [2 a + (n - 1) d]

= \frac{8}{2} [2 \times 30^{\circ} + (8 - 1) 30^{\circ}]

= 4 [60^{\circ} + 210^{\circ}]

= 4 \times 270^{\circ}

= 1080^{\circ}

∴

Sum of interior angles

= 1080^{\circ}

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Question Text	The interior angles of an octagon are in A.P. The smallest angle is $30^{\circ}$ and the common difference is $30^{\circ}$ .Find the sum of all the angles.
Answer Type	Text solution:1
Upvotes	150