Question

the supplementary of the angle is 10° more than three times ita complement . find the angle​

Answer 1

Question :-

The supplementary of the angle is 10° more than three times its complement . find the angle​.

Answer :-

The angle is 50°

Given :-

The supplementary of the angle is 10° more than three times its complement.

To find :-

The angle

Solution :-

     Let the angle be x°

$\underline{\underline{\textbf{Supplementary angles :}}}$

•    Two angles are called supplementary angles if the sum of the angles is equal to 180°

•    The supplementary angle of x° = (180 - x)°

$\underline{\underline{\textbf{Complementary angles :}}}$

•     Two angles are called complementary angles if the sum of the angles is equal to 90°

•     The complementary angle of x° = (90 - x)°

Given,

The supplementary of the angle is 10° more than three times its complement.

       (180 - x)° = 3(90 - x)° + 10°

         180° - x° = 270° - 3x° + 10°

             -x° = 270° - 180° -3x° + 10°

             3x° - x° = 90° + 10°

               2x° = 100°

                 x° = 100°/2

                 x° = 50°

>>> The angle is 50°