Question

In the figure, lines $l_1$ and $l_2$ instersect at O, forming angles as shown in the figure. If x = 45, find the values of y,z and u.

Answer 1

Two lines $l_1$ and $l_2$ intersect each other at O
$\angle x={45}^{\circ }$
$\because \angle z=\angle x$ (Vertically opposite angles)
= ${45}^{\circ }$
But $x+y={180}^{\circ }$ (Linear pair)
$\Rightarrow {45}^{\circ }+y={180}^{\circ }\Rightarrow y={180}^{\circ }-{45}^{\circ }={135}^{\circ }$
But u=y (Vertically opposite angles)
$\therefore u={135}^{\circ }$
Hence $y={135}^{\circ },z={45}^{\circ }$ and $u={135}^{\circ }$