Question

Angles of a quadrilateral are in the ratio $1:2:3:4$. Find all angles. What special name can you give to this quadrilateral and why?

Answer 1

$\Rightarrow$ Let the measure of angles be $x,2x,3x$ and $4x$.

We know that sum of measure of all four angles is ${360}^o.$

$\therefore$ $x+2x+3x+4x={360}^o$

$\Rightarrow$ $10x={360}^o$

$\Rightarrow$ $x={36}^o$

$\Rightarrow$ $2x=2\times {36}^o={72}^o$

$\Rightarrow$ $3x=3\times {36}^o={108}^o$

$\Rightarrow$ $4x=4\times {36}^o={144}^o$

$\Rightarrow$ The measures of angles of quadrilateral are ${36}^o,{72}^o,{108}^o$ and ${144}^o$.

$\Rightarrow$ We can see measure of all $4$ angles are different so, the given quadrilateral is trapezium.