If the angles of a quadrilateral are in A.P. | vedclass

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Question

(b) Suppose that $\angle A = {x^0}$, then $\angle B = x + {10^o}$,

$\angle C = x + {20^o}$and $\angle D = x + {30^o}$

So, we know that $\angle A

Vedclass · Accepted Answer

${75^o},\,{85^o},\,{95^o},\,{105^o}$

Vedclass · Answer

(b) Suppose that $\angle A = {x^0}$, then $\angle B = x + {10^o}$,

$\angle C = x + {20^o}$and $\angle D = x + {30^o}$

So, we know that $\angle A + \angle B + \angle C + \angle D = 2\pi $

Putting these values, we get

$({x^o}) + ({x^o} + {10^o}) + ({x^o} + {20^o}) + ({x^o} + {30^o}) = {360^o}$

$ \Rightarrow x = {75^o}$

Hence the angles of the quadrilateral are ${75^o},\;{85^o},\;{95^o},\;{105^o}$.

Trick : In these type of questions, students should satisfy the conditions through options.

Here $(b)$ satisfies both the conditions

$i.e.$ angles are in $A.P.$ with common difference ${10^o}$ and sum of angles is ${360^o}$.

If the angles of a quadrilateral are in $A.P.$ whose common difference is ${10^o}$, then the angles of the quadrilateral are

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