Question

Three angles of a quadrilateral are in the ratio $2:3:5$ and the fourth angles in ${90}^{\circ }$. Find the measures of the other three angles.

Answer 1

Three angle of quadrilateral are in ratio $2:3:5$

and fourth angle$={90}^o$

Let angle $2:3:5=k$ (constant)

and sum of angle in quadrilateral $=360$

$\angle 1+\angle 2+\angle 3+\angle 4=360$

$2k+3k+5k+{90}^o=360$

$10k={270}^o$

$R={27}^o$

$\angle 1=2k=2\times 27$

$={54}^o$

$\angle 2=3k=3\times 27$

$={81}^o$

$\angle 3=5k=5\times 27$

$={135}^o$