In the parallelogram abcd, the obtuse angle bisector intersects side bc at point k and makes an angle

In the parallelogram abcd, the obtuse angle bisector intersects side bc at point k and makes an angle with this side equal to 56 Find the acute angle of the parallelogram.

In a parallelogram, the bisector DK divides the ADC angle into two equal angles.

Since point K lies on the side BC of the parallelogram, the angle CKD and the angle ADK will be internal crosswise with two parallel lines AD and BC and the secant DK.

Hence the angle CKD = angle ADK and equal to 56⁰.

Then the angle of the parallelogram is ADC = 56 + 56 = 112⁰.

So the acute angle of the parallelogram is 180 – 112 = 68⁰.

Answer: 68⁰