SOLUTION: ABCD is a parallelogram. AP and BP are BISECTORS of angle DAB AND ANGLE CBA RESPECTIVELY. Intersecting each other at P. FIND ANGLE APB

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Question 1106496: ABCD is a parallelogram. AP and BP are BISECTORS of angle DAB AND ANGLE CBA RESPECTIVELY. Intersecting each other at P. FIND ANGLE APB
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52921) (Show Source):
You can put this solution on YOUR website!
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Answer. This angle is the right angle.

Proof.

In the triangle APB the sum of the angles ABP and PAB is half the sum of angles A and B of the parallelogram. The sum of these angles A and B is 180 degrees, as they are consecutive angles of the parallelogram. Hence, . . . and so on . . . et cetera . . .

Answer by greenestamps(13216) (Show Source):
You can put this solution on YOUR website!

(1) Angles A and B are consecutive angles in a parallelogram, so their sum is 180 degrees.
(2) Angle PAB is half of angle A; angle PBA is half of angle B.
(3) So the sum of angles PAB and PBA is 90 degrees.
(4) That makes angle APB 90 degrees.