In parallelogram ABCD, diagonal BD is the bisector of angle ABC. What is the BAD angle in degrees if the ADB

In parallelogram ABCD, diagonal BD is the bisector of angle ABC. What is the BAD angle in degrees if the ADB angle is 57 degrees.

1. Let us denote the angle by the symbol ∠.

2. Diagonal ВD, which is a bisector, divides ∠В into two equal angles: ∠ABD and ∠СВD.

3. ∠ADB = CBD, as angles at parallel sides ВС and АD (in a parallelogram the sides opposite to each other are parallel) and crossing them with diagonal ВD.

4. Consequently, ∠ABD = 57 °.

5. We calculate the degree measure ∠BAD, taking into account that the total value of all angles of the triangle ABD is 180 °:

∠BAD = 180 ° – ∠ABD – ∠ADB = 180 – 57 ° – 57 ° = 66 °.

Answer: ∠ВАD = 66 °.