- Home
- Standard 11
- Mathematics
If the angles of a quadrilateral are in $A.P.$ whose common difference is ${10^o}$, then the angles of the quadrilateral are
${65^o},\,{85^o},\,{95^o},\,{105^o}$
${75^o},\,{85^o},\,{95^o},\,{105^o}$
${65^o},\,{75^o},\,{85^o},\,{95^o}$
${65^o},\,{95^o},\,{105^o},\,{115^o}$
Solution
(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 ${360^o}$.
