Question

The angles of a octagon are in the ratio of 1:2:3:4:5:6:7:8 . Find the smallest angle

Answer 1

Answer:

Smallest angle= 30 degrees

Step-by-step explanation:

1x+2x+3x+4x+5x+6x+7x+8=1080              (ASP of octagon)

36x=1080

x=1080/36

x=30

The smallest angle is, 1*30=30 degrees

Hope this helps.................

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Answer 2

The smallest angle in given Octagon is 30°

Given:

The angles of an octagon are in the ratio of 1: 2: 3: 4: 5: 6: 7: 8

To find:

Find the smallest angle  

Solution:

Formula used:

Sum of interior angles = [n - 2] × 180°

Let x, 2x, 3x, 4x, 5x, 6x, 7x, and 8x be the interior angles of the Octagon

[ Since they are in 1: 2: 3: 4: 5: 6: 7: 8 ratio ]

Sum of angles = x + 2x + 3x + 4x + 5x + 6x + 7x + 8x = 36x  

Using the above formula

Sum of angles in a Octagon = [8 - 2] × 180°

= [6] × 180° = 1080°    

From above calculations

=> 36x = 1080°    

=> x = 1080°/36

=> x = 30°  

Therefore,

The smallest angle is 30°

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