Find the value of the acute angle of the parallelogram ABCD if the bisector of angle A makes

Find the value of the acute angle of the parallelogram ABCD if the bisector of angle A makes an angle of 43 degrees with side BC.

1. Suppose we have a bisector AM, which makes an angle of 43 ° with side BC;

2. AM is a secant of two parallel lines BC and AD. Hence ∠AMB = ∠MAD = 43 °;

3. Sharp ∠A = ∠MAD * 2 = 43 ° * 2 = 86 °;

4. Answer: the sharp ∠A of the parallelogram ABCD is 86 °.