The sum of an angle and half of its complementary angle is 75°. The measure of the angle is
(a) 40°
(b) 50°
(c) 60°
(d) 80°

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Solution

Let the required angle be x.
Now, complementnary of the required angle = 90^∘− x
Then,
$x + \frac{1}{2} (90 ° - x) = 75 ° \Rightarrow 2 x + 90 ° - x = 150 ° \Rightarrow x = 150 - 90 ° \Rightarrow x = 60 °$
Hence, the correct answer is option (c).

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The sum of an angle and half of its complementary angle is 75°. The measure of the angle is (a) 40° (b) 50° (c) 60° (d) 80°

Let the required angle be x. Now, complementnary of the required angle = 90∘ − x Then, x+1290°-x=75°⇒2x+90°-x=150°⇒x=150-90°⇒x=60° Hence, the correct answer is option (c).

The sum of an angle and half of its complementary angle is 75°. The measure of the angle is
(a) 40°
(b) 50°
(c) 60°
(d) 80°

Let the required angle be x.
Now, complementnary of the required angle = 90^∘− x
Then,
$x + \frac{1}{2} (90 ° - x) = 75 ° \Rightarrow 2 x + 90 ° - x = 150 ° \Rightarrow x = 150 - 90 ° \Rightarrow x = 60 °$
Hence, the correct answer is option (c).