(B) Let the angles of the quadrilateral be $x^o, (x+10)^o, (x+20)^o,$ and $(x+30)^o$.The sum of the interior angles of a quadrilateral is $360^o$.Ther

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(B) Let the angles of the quadrilateral be $x^o, (x+10)^o, (x+20)^o,$ and $(x+30)^o$.The sum of the interior angles of a quadrilateral is $360^o$.Therefore,$x + (x+10) + (x+20) + (x+30) = 360$.$4x + 60 = 360$.$4x = 300$.$x = 75^o$.The angles are $75^o, 85^o, 95^o,$ and $105^o$.Thus,option $(b)$ is correct.

Class 11 Mathematics Sequences and Series Arithmetic progression

Medium

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

A
$65^o, 85^o, 95^o, 105^o$
B
$75^o, 85^o, 95^o, 105^o$
C
$65^o, 75^o, 85^o, 95^o$
D
$65^o, 95^o, 105^o, 115^o$

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Sequences and Series

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Arithmetic progression

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DifficultKVPY 2012

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JEE MAIN 2022

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Given an $A.P.$ whose terms are all positive integers. The sum of its first nine terms is greater than $200$ and less than $220$. If the second term is $12$,then its $4^{th}$ term is:

DifficultJEE MAIN 2014

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Medium

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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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Let $f: R \rightarrow R$ be such that for all $x \in R$,the terms $(2^{1+x}+2^{1-x})$,$f(x)$,and $(3^x+3^{-x})$ are in $A.P.$. Then the minimum value of $f(x)$ is:

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