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 .
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