Question

In the given figure three lines $\overleftrightarrow{AB},\overleftrightarrow{CD}$ and $\overleftrightarrow{EF}$ intersecting at $O$. Find the values of $x,y$ and $z$ it is being given that $x:y:z=2:3:5$

Answer 1

$x:y:z=2:3:5$

let the angles be $2u,3u$ and $5u$

$\angle BOF=\angle AOE=x^{\circ }=2u$ (Alternete angles)

$\angle EOD=\angle COF=y^{\circ }=3u$ (Alternete angles)

$\angle AOC=\angle DOB=z^{\circ }=5u$ (Alternete angles)

$\angle EOD+\angle DOB+\angle BOF+\angle FOC+\angle COA+\angle AOE+\angle ={360}^{\circ }$

$3u+5u+2u+3u+5u+2u={360}^{\circ }$

$20u={360}^{\circ }$

$u=\frac{{360}^{\circ }}{20}={18}^{\circ }$

$x=2\times {18}^{\circ }={36}^{\circ }$

$y=3\times {18}^{\circ }={54}^{\circ }$

$z=5\times {18}^{\circ }={90}^{\circ }$