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8. sequence and series — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS8. sequence and series1 Mark
MCQ
If the angles of a quadrilateral are in $A.P.$ whose common difference is ${10^o}$, then the angles of the quadrilateral are
  • A
    ${65^o},\,{85^o},\,{95^o},\,{105^o}$
  • ✓
    ${75^o},\,{85^o},\,{95^o},\,{105^o}$
  • C
    ${65^o},\,{75^o},\,{85^o},\,{95^o}$
  • D
    ${65^o},\,{95^o},\,{105^o},\,{115^o}$
✓

Answer

Correct option: B.
${75^o},\,{85^o},\,{95^o},\,{105^o}$
b
(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 ${360^o}$.

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