Question

In parallelogram ABCD 3 multiple angle A equal to 2 multiple angle B then find angle D

Answer 1

In a parallelogram, the opposite angles are equal in magnitude. So angle A equals angle C, and angle B equals angle D.

(If you are wondering why the opposite angles are equal in magnitude, try drawing the diagonals AC and BD in a diagram of a parallelogram ABCD, then use congruent triangles. It is a rewarding exercise).

Let angle B = angle D = x degrees.

Then angle A = angle C = 2x degrees.

Since a parallelogram is a quadrilateral, the angles in a parallelogram add to 360 degrees,

So angle A + angle B + angle C + angle D = 360 degrees

So 2x+x+2x+x = 360

x=60 degrees so angles B and D are 60 degrees.

2x = 120 degrees so angles A and C are 120 degrees.