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