Question

Among the two supplementary angles, the measure of the larger angle is 36º more than the measure of smaller. Find their measures

Answer 1

We know that, if the sum of two angles is equal to 180°, then they are called supplementary angles.
Given, sum of two angles = 180°
           difference of two angles = 36°
Let, x be the larger angle and,
       y be the smaller angle
Then, x = y + 36°
As we know,
                                       x + y = 180°
Applying the relation between x and y,
                                   y + 36° + y = 180°
                                     2y + 36° = 180°
                                          2y = 144°
                                         y = 144°/ 2
                                            y = 72°
Then substitute y value in any of the equation,
                                         x = y + 36°
                                       x = 72° + 36°
                                          x =108°
∴ The required angles are = 108°, 72°

Hope my answer helps you : )