Mathematics

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


SOLUTION
Given, $$x=45^o$$

As per the diagram, two lines $$l_1$$ & $$l_2$$ intersected to form two pairs of vertically opposite angles.

$$x = z$$  -- (1)

$$u = y$$  --(2)

From (1)

$$x = z=45^o$$ .

We also know that the sum of all the angles around a point is $$360^o$$

$$x+u+z+y=360^o$$

$$45+u+45+u=360^o$$

$$90+2u=360^o$$

$$2u=270^o$$

$$u=135^o$$

=>$$y=135^o$$

$$\therefore$$ $$x = 45^o, z=45^o, u=135^o$$ and $$y=135^o$$.
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Subjective Medium Published on 09th 09, 2020
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