If all interior angle of quadrilateral are in A.P. If common difference is 10^o , then find smallest

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8. Sequences and Series

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If all interior angle of quadrilateral are in $A.P.$ If common difference is $10^o$, then find smallest angle ? .............. $^o$

A

$60$

B

$70$

C

$120$

D

$75$

Solution

Let Angles are $\rightarrow a-3 d, a-d, a+d, a+3 d$

common difference $\Rightarrow 2 \mathrm{d}=10^{\circ} \Rightarrow \mathrm{d}=5^{\circ}$

$ \operatorname{sum} \Rightarrow 4 a=360 $

$ a =90^{\circ} $

so smallest Angle $\Rightarrow a-3 d=90-3 \times 5^{\circ}=75^{\circ}$

Standard 11

Mathematics

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(JEE MAIN-2018)