Question

Please i need answer fast

Answer 1

Step-by-step explanation:

we know that sum of adjacent angle = 180

angle DAB + angle CBA = 180

O is bisector of angle A,angle B

1/2(DAB + CBA) =1/2* 180

OAB +OBA = 90

OAB + OBA + BOA =180

BOA = 180-90

BOA = 90

Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

$\rm :\longmapsto\:OA \: bisects \: \angle \:BAD$

$\rm :\implies\:\angle \:DAO \: = \: \angle \:OAB \: = \: x \: - - (1)$

Also,

$\rm :\longmapsto\:OB \: bisects \: \angle \:CBA$

$\rm :\implies\:\angle \:CBO \: = \: \angle \:OBA \: = \: y \: - - (2)$

Now,

• In parallelogram ABCD,

We know,

• Sum of adjacent angle is supplementary.

$\rm :\implies\:\angle \:BAD + \angle \:CBA = 180 \degree \:$

$\rm :\implies\:2x + 2y = 180\degree \:$

$\bf\implies \:x + y = 90\degree \: - - (3)$

Now,

$\rm :\longmapsto\:In \: \triangle \: AOB$

$\rm :\longmapsto\:\sf \: As \: sum \: of \: angles \: of \: a \: triangle \: is \:180\degree \:$

$\rm :\longmapsto\:\angle \:OAB + \angle \:OBA + \angle \:AOB = 180\degree \:$

$\rm :\longmapsto\:x + y + \angle \:AOB = 180\degree \:$

$\rm :\longmapsto\:90\degree \: + \angle \:AOB = 180\degree \:$

$\bf\implies \:\angle \:AOB = 90\degree \:$

Additional Information :-

• The opposite sides are parallel and equal.

• The opposite angles are equal.

• The sum of adjacent angles are supplementary

• If anyone of the angles is a right angle, then parallelogram is a rectangle.

• The two diagonals bisect each other

• Each diagonal bisects the parallelogram into two congruent triangles

• Sum of square of all the sides of parallelogram is equal to the sum of square of its diagonals. It is called parallelogram law