Question

In parallelogram ABCD, AP and BP are the angular bisector of angle BAD and angle ABC. Show that angle APB = 90 degrees. Please consult the inage above.​

Answer 1

Explanation:

In an quadrilateral, the interior angles always add to be 360 degrees. Due to this, we can infer that 2 adjacent angles in a parallelogram will add to be 180 degrees.

Lets say that Angle DAB = 120 degrees and angle ABC = 60 degrees. If Line AP and PB are angular bisectors, then divide each of the angles by 2, and add them together.

120 / 2 = 60 degrees

60 / 2 = 30 degrees

30 + 60 = 90 degrees

This also works for any angle measures of DAB and ABC, as long as they add up to be 180. I just used simple measurements to demonstrate my calculation.