ABCD is a parallelogram the angle bisector of angleA and angleD intersect at O. Find the measure of angle AOD

Answer 1

Did you make your sketch?
let angle A be 2x
let angle D be 2y
because of the parallel lines,
2x + 2y = 190
x + y = 90

after bisection of angle A and D
look at triangle AOD
we have x + y + angle AOD = 180
90 + angle AOD = 180
angle AOD = 90°