Question

diagonals of quadrilateral ABCD is bisect each other angle A=35degree determine angle B

Answer 1

As there is bisection of diagonals, Therefore ABCD is parallelogram

angle A+ angle B=180 (adjacent angles of parallelogram are supplementary)

angle B= 180-35=145

Answer 2

Given :  diagonals of quadrilateral ABCD  bisect each other angle A=35°

To Find : angle C and angle B

Solution:

diagonals of quadrilateral ABCD  bisect each other

=> ABCD is a parallogram

Opposite angle in parallelogram are equal

Hence ∠C = ∠A

∠A = 35°

=> ∠C =  35°

Sum of adjacent angles = 180°

=> ∠A + ∠B = 180°

=>  35°  + ∠B = 180°

=> ∠B = 145°

if u do not want to use direct

then let say Diagonal bisect at O

=> AO = CO    and  BO = DO

and ∠AOB = ∠COD     and ∠AOD = ∠BOC  ( Vertically opposite angles)

then using SAS    ΔAOB ≅ ΔCOD  => ∠OAB  = ∠OCD

∠BOC ≅ ΔDOA  => ∠OAD  = ∠OCB

=> ∠OAB +  ∠OAD = ∠OCD + ∠OCB

=> ∠A = ∠C

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