If the supplementary of an angle is equals to the complementary of tha

1.	If the supplementary of an angle is equals to the complementary of that supplementary angle, then the angle is A) 135° B) 45° C) 90° D) 60°
Answer» Correct option is (A) 135° Let the required angle be x. \(\therefore\) Its supplementary angle is \(180^\circ-x.\) Now, complementary angle of \(180^\circ-x\) is \(90^\circ-(180^\circ-x)\) \(=x-90^\circ\) According to given condition, \(180^\circ-x=x-90^\circ\) \(\Rightarrow\) 2x = \(180^\circ+90^\circ=270^\circ\) \(\Rightarrow\) x = \(\frac{270^\circ}2=135^\circ\) Correct option is A) 135°

If the supplementary of an angle is equals to the complementary of that supplementary angle, then the angle is A) 135° B) 45° C) 90° D) 60°

Answer»

Correct option is (A) 135°

Let the required angle be x.

\(\therefore\) Its supplementary angle is \(180^\circ-x.\)

Now, complementary angle of \(180^\circ-x\) is \(90^\circ-(180^\circ-x)\)

\(=x-90^\circ\)

According to given condition,

\(180^\circ-x=x-90^\circ\)

\(\Rightarrow\) 2x = \(180^\circ+90^\circ=270^\circ\)

\(\Rightarrow\) x = \(\frac{270^\circ}2=135^\circ\)

Correct option is A) 135°