Find the value of x for which the angles $(2 x - 5)^{\circ}$ and $(x - 10)^{\circ}$ are the complementary angles.

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Solution

Two angles whose sum is 90° are called complementary angles.
It is given that the angles (2x – 5)° and ( x – 10)° are the complementary angles.
∴ (2x – 5)° + ( x – 10)° = 90°
⇒ 3x° – 15° = 90°
⇒ 3x° = 90° + 15° = 105°
⇒ x° = $\frac{105}{3}$ = 35°
Thus, the value of x is 35.

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