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Question

In figure, find the values of $$x, y$$ and $$z$$.

Solution
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As per the diagram there are two pairs of vertically opposite angles.
and we know that vertically opposite angles are equal.
$$y = 25^o$$
$$x^o = z^o$$
and we know that. sum of all the angles around a point is $$360^o$$.
$$y^o+x^o+25^o+z^o=360^o $$
$$25^o+x^o+25^o+x^o=360^o $$
$$50^o+2x^o=360^o $$
$$25^o+x^o=180^o $$
$$x^o=155^o $$
$$ \therefore $$ $$x=155^o $$, $$y=25^o $$ and $$z=155^o $$,

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