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

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

Competitive Quantitative Aptitude Progression and Sequence Progression and Sequence

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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The sums of $n$ terms of two arithmetic series are in the ratio $(2n + 3) : (6n + 5)$. Find the ratio of their $13^{th}$ terms.

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Sum the series $51 + 50 + 49 + \ldots + 21$.

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If $S$ is the sum to infinity of a $G.P.$,whose first term is $a$,then the sum of the first $n$ terms is

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Which number should be added to the numbers $13, 15, 19$ so that the resulting numbers are the consecutive terms of a $H.P.$?

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In a geometric progression,if the ratio of the sum of first $5$ terms to the sum of their reciprocals is $49$,and the sum of the first and the third term is $35$. Then the first term of this geometric progression is

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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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The sums of $n$ terms of two arithmetic series are in the ratio $(2n + 3) : (6n + 5)$. Find the ratio of their $13^{th}$ terms.

Sum the series $51 + 50 + 49 + \ldots + 21$.

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