# In a quadrilateral angles are in the ratio 2:3:4:7 . Find all the angles of the quadrilateral. Is it a convex or a concave quadrilateral

Given: The angles of a quadrilateral are in ratio $2:3:4:7$

To do: To Find the measure of each angle of the quadrilateral and to find the type of quadrilateral.

Solution:

Let $ABCD$ be a quadrilateral and $x$ be the common in given ratio such that:

$\angle A=2x,\ \angle B=3x,\ \angle C=4x,\ \angle D=7x$

As known that the sum of all the angles of quadrilateral is $360^o$.

$\Rightarrow \angle A+\angle B+\angle C+\angle D=360^o$

$\Rightarrow 2x+3x+4x+7x=360^o$

$\Rightarrow 16x=360^o$

$\Rightarrow x=\frac{360}{16}$

$\Rightarrow x=22.5^o$

$\Rightarrow \angle A=2x=2\times22.5=45^o$

$\Rightarrow \angle B=3x=3\times22.5=67.5^o$

$\Rightarrow \angle C=4x=4\times22.5=90^o$

$\Rightarrow \angle D=7x=7\times22.5=157.5^o$

This is a convex type quadrilateral because measure of all the angles are less than $180^o$.

Updated on: 10-Oct-2022

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