Question

The average of $3$ angles of a quadrilateral which are in the ratio of $2:4:5$ is ${77}^o$. Find all the angles of the quadrilateral.

Answer 1

Let $2x,4x$ and $5x$ be the $3$ angles of given quadrilateral and $m$ be the fourth angle of the same quadrilateral.

Therefore,

$\frac{2x+4x+5x}{3}=77$

$\Rightarrow 11x=231$

$\Rightarrow x=\frac{231}{11}=21$

Therefore,

$2x=2\times 21=42$

$4x=4\times 21=84$

$5x=5\times 21=105$

The three angles of the quadrilateral are ${42}^o,{84}^o$ and ${105}^o$.

Therefore,

As we know that sum of internal angles of a quadrilateral is ${360}^o$.

$\therefore 42+84+105+m=360$

$\Rightarrow m=360-231={129}^o$

Hence the angles of the given quadrilateral are ${42}^o,{84}^o,{105}^o$ and ${129}^o$.

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