Q. 25.0( 1 Vote )

ABCD is a cyclic quadrilateral. Given that ADB + DAB = 120°and ABC + BDA = 145°. Find the value of CDB


A. 75°

B. 115°

C. 35°

D. 45°

Answer :

As ADB + DAB = 120°


In triangle ABD as sum of all angles = 180°


ABD = 180–120 = 60°


As ABCD is cyclic, opposite angles have sum of 180°


Let BAD = x°


Hence BCD = 180–x


Let BDC = a°


Let DBC = z°; ABC = 60 + z


Let ADB = y°


As sum of angles of triangle BDC = 180°


180–x + a + z = 180


a = x–z ...(1)


According to question,


x + y = 120 ..(2)


and


60 + z + y = 145...(3)


Subtracting (3) from (2)


We get


x + y–60–z–y = –25


x–z = 35


Equating from (1) we get


a = 35°


hence CDB = 35°

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