Question

In a quadrilateral three angles are in the ratio $3:3:1$ and one of the angles is ${80}^{\circ }$, then other angles are :

• A. ${120}^{\circ },{120}^{\circ },{40}^{\circ }$
• B. ${100}^{\circ },{100}^{\circ },{80}^{\circ }$
• C. ${110}^{\circ },{110}^{\circ },{60}^{\circ }$
• D. ${90}^{\circ },{90}^{\circ },{30}^{\circ }$

Answer 1

The correct option is A ${120}^{\circ },{120}^{\circ },{40}^{\circ }$

In figure $ABCD$ is a quadrilateral.

We have given ratio of three angle $3:3:1$.

Let $\angle A=3x,\angle B=3x,\angle C=x$ and $\angle D={80}^{\circ }$.

We know, by angle sum property, the sum of all interior angles of quadrilateral is ${360}^{\circ }$]

$\Rightarrow$ $\angle A+\angle B+\angle C+\angle D={360}^{\circ }$

$\Rightarrow$ $3x+3x+x+{80}^{\circ }={360}^{\circ }$

$\Rightarrow$ $7x={280}^{\circ }$

$\therefore$ $x={40}^{\circ }=\angle C$. ---- ( 1 )

$\Rightarrow$ $\angle A=3x=3\times {40}^{\circ }={120}^{\circ }$ -- ( 2 )

$\Rightarrow$ $\angle B=3x=3\times {40}^{\circ }={120}^{\circ }$ -- ( 3 )

From ( 1 ), ( 2 ) and ( 3 ),

$\Rightarrow$ Other angles are ${120}^{\circ },{120}^{\circ },{40}^{\circ }$.

Hence, option $A$ is correct.