Question

Four angles of a quadrilateral are in the ratio $3:5:7:9$. The greatest angle is _________.

• A. ${125}^o$
• B. ${75}^o$
• C. ${135}^o$
• D. ${120}^o$

Answer 1

Answer: (C)

${135}^o$

Let the angles of quadrilateral be $x,y,z,w.$

Given ,$x:y:z:w=3:5:7:9$

$x=3k$

$y=5k$

$z=7k$

$w=9k$

we k.n.t sum of angles of a quadrilateral is ${360}^{\circ }$

$x+y+z+w=3k+5k+7k+9k={360}^{\circ }$

$\Rightarrow 24k={360}^{\circ }$

$\Rightarrow k=\frac{{360}^{\circ }}{24}={15}^{\circ }$

Greatest angle is $w=9k=9\left({15}^{\circ }\right)={135}^{\circ }$