Question

In figure, three coplanar lines intersect at a point O, forming angles as shown in the figure. Find the values of $x,y,z$ and $u$.

Answer 1

Since vertically opposite angles are equal,

$\therefore \angle BOD=\angle COA\text{and}\angle DOF=\angle COE$

$\Rightarrow \angle BOD=z={90}^{\circ }\text{and}\angle DOF=y={50}^{\circ }$

As, AB is a straight line

$x+y+z={180}^{\circ }\left(\text{Linear pair}\right)$

$x+{50}^{\circ }+{90}^{\circ }={180}^{\circ }$

$x={180}^{\circ }-{140}^{\circ }$

$x={40}^{\circ }$

$\text{Also},u=x\left(\text{Vertically opposite angles}\right)$

$\Rightarrow u={40}^{\circ }$

Hence, the values of $x={40}^{\circ },y={50}^{\circ },z={90}^{\circ }$ and $u={40}^{\circ }$.