Question

in cyclicAl quadrilateral abcd ,ab parallel to cd.if angle b=80, find other angle of abcd
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Answer 1

Answer:

IWe know that the sum of the opposite angles of a cyclic quadrilateral is 180o. In the cyclic quadrilateral ABCD, angles A and C and the angle B and D form pairs of opposite angles.

∴∠A+∠C=180o and ∠B+∠D=180o

⇒2x−1+2y+15=180 

      and y+5+4x−7=180

⇒2x+2y=166 

      and 4x+y=182

⇒x+y=83 ..(i)

and, 4x+y=182 ..(ii)

Subtracting equation (i) from equation (ii), we get

3x=99⇒x=33

Substituting x=33 in equation (i), we get y=50

Hence, ∠A=(2×33−1)o=65o,∠B=(y+5)o=(50+5)o=55o

∠C=(2y+15)o=(2×50+15)o=115o and ∠D=(4×33−7)o=125o.