In the adjoining figure three coplanar lines AB, CD, EF intersect at a

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