Question

The difference between an angle and its complement is 10° find measure of the larger angle.

Answer 1

Let the angle be x and its complement be y, where x > y.

Sum of complementary angles is 90°.

∴ x + y = 90°      ......(i)

According to the given condition,

The difference between an angle and its complement is 10°

∴ x – y = 10°    ......(ii)

Adding equations (i) and (ii), we get

   x + y = 90° 
+ x – y = 10°     
 2x       = 100°

∴ x = `(100^circ)/2` = 50°

∴ The larger angle is 50°.