Mathematics

In Fig., ACB is a line such that $$ \angle DCA = 5x $$ and $$ \angle DCB = 4x.$$ Find the values of $$ \angle DCA $$ and $$ \angle DCB.$$


ANSWER

$$ \angle DCA = 100^{\circ};\angle DCB = 80^{\circ}$$


SOLUTION
Here, $$ACB$$ is a line.
$$\Rightarrow$$  $$\angle DCA+\angle DCB=180^o$$               [ Linear pair ]
$$\Rightarrow$$  $$5x+4x=180^o$$
$$\Rightarrow$$  $$9x=180^o$$
$$\Rightarrow$$  $$x=\dfrac{180^o}{9}$$
$$\Rightarrow$$  $$x=20^o$$
$$\Rightarrow$$  $$\angle DCA=5x=5\times 20^o=100^o$$
$$\Rightarrow$$  $$\angle DCB=4x=4\times 20^o=80^o$$

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