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Question -

If an angle is 30° more than one half of its complement, find the measure of the angle.



Answer -

Let the measure of the required angle = x
∴  Its complement =  90° – x
∴  x = (90° – x) + 30°
2x = 90° – x + 60°
⇒ 2x + x = 90° + 60°
⇒  3x = 150°
⇒ x = = 50°
∴ Required angle = 50°

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