The difference between two complementary angles is 10° then the large

1.	The difference between two complementary angles is 10° then the largest angle is …………………..A) 40° B) 50° C) 70° D) 60°
Answer» Correct option is B) 50° Correct option is (B) 50° Let complementary angles are x & y. \(\therefore\) x+y = \(90^\circ\) _________(1) \((\because\) Sum of complementary angles is \(90^\circ)\) Also, x - y = \(10^\circ\) _________(2) (Given) Subtract equation (2) from (1), we get (x+y) - (x - y) = \(90^\circ\) - \(10^\circ\) \(\Rightarrow\) 2y = \(80^\circ\) \(\Rightarrow\) y = \(\frac{80^\circ}2=40^\circ\) From (1), x = \(90^\circ\) - y = \(90^\circ\) - \(40^\circ\) = \(50^\circ\) Hence, \(40^\circ\) & \(50^\circ\) are required complementary angles. \(\therefore\) Largest angle = \(50^\circ\).

The difference between two complementary angles is 10° then the largest angle is …………………..A) 40° B) 50° C) 70° D) 60°

Answer»

Correct option is B) 50°

Correct option is (B) 50°

Let complementary angles are x & y.

\(\therefore\) x+y = \(90^\circ\) _________(1) \((\because\) Sum of complementary angles is \(90^\circ)\)

Also, x - y = \(10^\circ\) _________(2) (Given)

Subtract equation (2) from (1), we get

(x+y) - (x - y) = \(90^\circ\) - \(10^\circ\)

\(\Rightarrow\) 2y = \(80^\circ\)

\(\Rightarrow\) y = \(\frac{80^\circ}2=40^\circ\)

From (1), x = \(90^\circ\) - y = \(90^\circ\) - \(40^\circ\) = \(50^\circ\)

Hence, \(40^\circ\) & \(50^\circ\) are required complementary angles.

\(\therefore\) Largest angle = \(50^\circ\).