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In the figure, three coplanar lines intersect at a point $O$, forming angles as shown in the figure. Find the values of $x, y, z$ and $u$.
"
Given:
Three coplanar lines intersect at a point $O$.
To do:
We have to find the values of $x, y, z$ and $u$.
Solution:
We know that,
Vertically opposite angles are equal.
Sum of the angles on a line is $180^o$.
Therefore,
$\angle BOD = 90^o, \angle DOF = 50^o$
$\angle BOD + \angle DOF + \angle FOA = 180^o$
$90^o + 50^o + u = 180^o$
$u = 180^o-140^o$
$u= 40^o$
$x = u =40^o$ (Vertically opposite angles)
$x+y+90^o=180^o$
$40^o+y=180^o-90^o$
$y=90^o-40^o$
$y=50^o$
$z = 90^o$ (Vertically opposite angles)
Hence, $x = 40^o, y = 50^o, z = 90^o$ and $u = 40^o$.
Updated on: 10-Oct-2022
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