In a quadrilateral $ABCD$, the angles $A, B, C$ and $D$ are in the ratio $1 : 2 : 4 : 5$. Find the measures of each angle of the quadrilateral.

Given:

In a quadrilateral $ABCD$, the angles $A, B, C$ and $D$ are in the ratio $1 : 2 : 4 : 5$.

To do:

We have to find the measures of each angle of the quadrilateral.

Solution:

We know that,

Sum of the angles in a quadrilateral is $360^o$.

Let the angles $A, B, C$ and $D$ be $x, 2x, 4x$ and $5x$ respectively.

Therefore,

$x+2x+4x+5x=360^o$

$12x=360^o$

$x=\frac{360^o}{12}$

$x=30^o$

This implies,

$2x=2(30^o)=60^o$

$4x=4(30^o)=120^o$

$5x=5(30^o)=150^o$

Hence, the measures of each angle of the quadrilateral are $30^o, 60^o, 120^o$ and $150^o$.

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Updated on: 10-Oct-2022

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