Mathematics

In Fig., $$POS$$ is a line, find $$x$$.


ANSWER

20


SOLUTION
$$POS$$ is a line.
$$\Rightarrow$$  $$\angle POQ+\angle QOS=180^o$$               [ Linear pair ]
$$\Rightarrow$$  $$\angle POQ+(\angle QOR+\angle ROS)=180^o$$
$$\Rightarrow$$  $$60^o+(4x+40^o)=180^o$$
$$\Rightarrow$$  $$100^o+4x=180^o$$
$$\Rightarrow$$  $$4x=80^o$$

$$\Rightarrow$$  $$x=\dfrac{80^o}{4}$$

$$\Rightarrow$$  $$x=20^o$$
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