Question

In a parallelogram ABCD, if ∠A = (3x − 20)°, ∠B = (y + 15)°, ∠C = (x + 40)°, then find the values of xand y.

Answer 1

In parallelogram ABCD, ∠A and ∠C are opposite angles.

We know that in a parallelogram, the opposite angles are equal.

Therefore,

∠C = ∠A

We have  ∠A = (3x - 20°) and ∠C = (x + 40°)

Therefore,

x + 40° = 3x - 20°

x - 3x = -40° - 20°

-2x = - 60°

x = 30°

Therefore,

∠A = (3x - 20°)

∠A = [3(30) - 20°]

∠A = 70°

Similarly,

∠C = 70°

Also, ∠B = ( y + 15)°

Therefore,

∠D = ∠B

∠D = (y + 15 )°

By angle sum property of a quadrilateral, we have:

                  ∠A + ∠B + ∠C + ∠D = 360°

70° +(y + 15)° + 70° + (y + 15)° = 360°

                      140° + 2 (y + 15)° = 360°

                                   2(Y + 15)° = 360° - 140°

                                   2(y + 15)° = 220°

                                     (y + 15)° = 110°

                                                 y = 95°

Hence the required values for x and y are 30° and 95° respectively.