Question

IN A PARALLELOGRAM ABCD,AO AND BO ARE THE ANGULAR BISECTORS OF TWO ADJACENT ANGLES OF THE BASE.WHAT IS THE MEASURE OF ANGLE AOB

Answer 1

hii dude here is ur answer

Answer 2

$\textbf{ Hello Mate! }$

Given : AO and BO are angle bidectors of angle A and B respectively in parallelogram.

Solution : As ABCD is parallelogram where AD || BC. So there sum of interior consecutive angle will be 180°.

< A + < B = 180°

On dividing equation by 2

x + y = 90° [ AO and BO are angle bisectors ]

In triangle AOB we have,

x + y + < AOB = 180° [ Angle sum property ]

90° + < AOB = 180°

< AOB = 180° - 90°

< AOB = 90°

$\boxed{ \textsf{ \red{ Measure\:of\:angle\:AOB\:is\:90° }}}$

[ Note : I have used "<" as angle for sake of convinience. ]

Have great future ahead!