Question

If the angles $(2x-10{)}^{\circ }$ and $(x-5{)}^{\circ }$ are complemeniary angles, find x.

Answer 1

First complementary angle = $(2x-{10}^{\circ })$ and second = $(x-5{)}^{\circ }$
$\therefore 2x-{10}^{\circ }+x-5^{\circ }={90}^{\circ }\Rightarrow 3x-{15}^{\circ }={90}^{\circ }\Rightarrow 3x={90}^{\circ }+{15}^{\circ }={105}^{\circ }$
$\therefore x=\frac{{105}^{\circ }}{3}={35}^{\circ }$
$\therefore$ First angle = $2x-{10}^{\circ }=2\times {35}^{\circ }-{10}^{\circ }$
=${70}^{\circ }-{10}^{\circ }={60}^{\circ }$ and second angle =$x-5={35}^{\circ }-5={30}^{\circ }$.