Question

In the adjoining figure three coplanar lines AB, CD, EF intersect at a point O, forming angles as shown. Find the value of x , y, ,z, t.

Answer 1

Answer:

             $x={40}^{o}, y={40}^{o}, z={50}^{o}, t={90}^{o}$

Solution:

When two lines intersect, the angles that are vertically opposite will be equal

Hence $\angle BOC=\angle AOD$

    ${ 90 }^{ o }=t$

$\angle DOF= \angle EOC$

 $Z= {50}^{o}$

Since AB is a straight line,

$\angle AOE + \angle EOC + \angle COB={180}^{o}$

$X + {50}^{o} + {90}^{o} = {180}^{o}$

$X = 180 - 140 = {40}^{o}$

As x and y are opposite vertical angles, $x=y={40}^{o}$

Therefore, $x={40}^{o}, y={40}^{o}, z={50}^{o}, t={90}^{o}$