Question

ABCD is a parallelogram the angle bisector of angle A and angle D intersect at O find the measure of a angle aod

Answer 1

here is the answer.

Answer 2

Given :

ABCD is a parallelogram the angle bisector of A and angle D

intersect at O.

To find :

m<AOD = ?

Explanation :

<A + <D = 180°

/* Adjacent angles in a parallelogram are supplementary */

divide each term by 2 , we get

=> <A/2 + <D/2 = 90°----(1)

Now ,

In ∆AOD ,

<OAD + <ODA + <AOD = 180°

/* Angle sum property */

=> <A/2 + <D/2 + <AOD = 180°

/* given */

=> 90° + <AOD = 180° [ from (1)]

=> <AOD = 180° - 90°

=> <AOD = 90°

Therefore,

<AOD = 90°

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