The bisector of one of the angles of the parallelogram, intersecting with its side, forms an angle with it equal

The bisector of one of the angles of the parallelogram, intersecting with its side, forms an angle with it equal to 32 degrees. Calculate the angles of a parallelogram

1. A, B, C, D – the tops of the parallelogram. BK – bisector to the AD side. Let us denote the angle by the symbol ∠. ∠АКB is equal to 32 °.

2. The bisector BK of the parallelogram ABCD cuts off the triangle ABK, which is isosceles. Therefore, ∠ AKB = ∠ABK = 32 °.

3. ∠ СВД = ∠АВК = 32 °, since the bisector BК divides ∠В into two equal parts. ∠В = 32 ° x 2 = 64 °.

4. The opposite angles of the parallelogram ∠D and ∠B are equal. ∠D = 64 °.

5.∠С = 180 ° – 64 ° = 116 °.

6.∠А = ∠С = 116 °

Answer: ∠А = ∠С = 116 °, ∠D = ∠В = 64 °.