Question

The angle of Quadrilateral are in AP. The smallest angle is 12. Find the angle of Quadrilateral ​

Answer 1

Heya !

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Given that :

The angles of a quadrilateral are in AP.

Smallest angle = 12°

Since there are 4 angles in a quadrilateral,

=> n = 4

=> First term ( a ) = 12

We also know,

Sun of angles of a quadrilateral = 360°

Then,

=> Sum = 360

Common difference ( d ) = ?

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S(n) = n/2 × { 2a + ( n - 1 )d }

=> 360 = 4/2 × { 2 × 18 + ( 4 - 1 )d }

=> 360 = 2 × { 36 + 3d }

=> 180 = 36 + 3d

=> 3d = 180 - 36

=> d = 144/3

=> d = 48

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Now ,

> First term = 18

> Second term = a + d

=> 18 + 48

=> 66

Third term = a + 2d

=> 18 + 96

=> 114

Fourth term = a + 3d

=> 18 + 144

=> 162

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The angles of the quadrilateral are :

18° , 66° , 114° and 162 °

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Thanks :)