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

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Solution

$∠$ BOD + $∠$ DOF + $∠$ FOA = 180° (Linear pair)
∴ $∠$ FOA = $∠$ u = $180 ° - 90 ° - 50 ° = 40 °$
$∠ FOA = ∠ x = 40 °$ (Vertically opposite angles)
$∠ BOD = ∠ z = 90 °$ (Vertically opposite angles)
$∠ EOC = ∠ y = 50 °$ (Vertically opposite angles)

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