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

A

$60$

B

$70$

C

$120$

D

$75$

Solution

Common differcuce in angle $(\phi)=10^{\circ}$ let $4$ angles in $A.P.$ area atd, $a+2d, a+3 d=$ and sum are,

$a+a+d+a+2 d+a+3 d=360^{\circ}$

$4 a+c d=360^{\circ}$

$4 a=360^{\circ}-6 d=360^{\circ}-60^{\circ}$

$4 a=380^{\circ}$

$a=75^{\circ}$

Standard 11

Mathematics

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