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In the figure, lines $l_1$ and $l_2$ intersect at $O$, forming angles as shown in the figure. If $x = 45$, find the values of $y, z$ and $u$.
"
Given:
Lines $l_1$ and $l_2$ intersect at $O$ and $x = 45^o$.
To do:
We have to find the values of $y, z$ and $u$.
Solution:
We know that,
Vertically opposite angles are equal.
Therefore,
$z = x = 45^o$ (Vertically opposite angles)
$x + y = 180^o$ (Linear pair)
$45^o + y= 180^o$
$y = 180^o - 45^o$
$y = 135^o$
$u = y = 135^o$ (Vertically opposite angles)
Hence, $y = 135^o, z = 45^o$ and $u = 135^o$.
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