Question

Diagonals of a quadrilateral ABCD bisect each other. If angle A=35*, determine angle B

Answer 1

145° because

180-35=145

Answer 2

Answer: B =55°

Step-by-step explanation:

In quadrilateral ABCD,

Diagonals bisect each other, so AE =EC AND BE= DE.

NOW, IN TRIANGLE AEB AND DEC,

DE = BE GIVEN

AE = EC GIVEN AND

ANGLE AEB = ANGLE DEC ( VERTICALLY OPPOSITE ANGLES) SO

THEY ARE CONGRUENT BY SAS RULE.

NOW, ANGLE EAB = ANGLE ECD( ALTERNATE INTERIOR ANGLES) BY CPCT. SO THE LINES AB AND CD ARE PARALLEL.

SIMILARLY TRIANGLE AED IS CONGRUENT TO TRIANGLE BEC BY SAS RULE. SO, BC IS PARALLEL TO AD.

IT IS GIVEN THAT ANGLE A = 35°. SO

ANGLE B + ANGLE A = 180°

(ANGLES ON THE SAME SIDE OF THE TRAVERSAL AB WITH PARALLEL LINES AD AND BC.)

SO,

35° + ANGLE B = 180°

ANGLE B = 180° - 35° = 145°.

HOPE THAT IT HELPS YOU.