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0 votes
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in Linear Equations by (38.9k points)

The difference between two complementary angles is 10° then the largest angle is …………………..

A) 40° 

B) 50° 

C) 70° 

D) 60°

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2 Answers

+1 vote
by (36.7k points)

Correct option is  B) 50°

0 votes
by (57.0k points)

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 = \(50^\circ\).

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