Mathematics

Compute the value of $$x$$ in each of the following figures


ANSWER

$$ 50^{\circ} $$


SOLUTION
$$\Rightarrow$$  $$\angle ACD+\angle ACB=180^o$$             [ Linear pair ]
$$\Rightarrow$$  $$110^o+\angle ACB=180^o$$
$$\therefore$$  $$\angle ACB=70^O$$
Again,
$$\Rightarrow$$  $$\angle ABE+\angle ABC=180^o$$          [ Linear pair ]
$$\Rightarrow$$  $$120^o+\angle ABC=180^o$$
$$\therefore$$  $$\angle ABC=60^o$$
Now, In $$\triangle ABC,$$
$$\Rightarrow$$  $$\angle ABC+\angle ACB+\angle BAC=180^o$$               [ Sum of angle of property of triangle ]
$$\Rightarrow$$  $$60^o+70^o+x=180^o$$
$$\Rightarrow$$  $$130^o+x=180^o$$
$$\Rightarrow$$  $$x=50^o$$
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