Find the value of x for which the angles
Question:

Find the value of x for which the angles (2x – 5)° and (x – 10)° are the complementary angles.

Solution:

Two angles whose sum is $90^{\circ}$ are called complementary angles.

It is given that the angles $(2 x-5)^{\circ}$ and $(x-10)^{\circ}$ are the complementary angles.

$\therefore(2 x-5)^{\circ}+(x-10)^{\circ}=90^{\circ}$

$\Rightarrow 3 x^{\circ}-15^{\circ}=90^{\circ}$

$\Rightarrow 3 x^{\circ}=90^{\circ}+15^{\circ}=105^{\circ}$

$\Rightarrow x^{\circ}=\frac{105^{\circ}}{3}=35^{\circ}$

Thus, the value of $x$ is 35 .