Question

plz anyone explain it with correct option

Answer 1

Given ∠A = 2 ∠B

         ∠ACD = 2 ∠DCB

In ΔABC

            ∠A + ∠B + ∠C = 180°

           2∠B + ∠B + ∠ACD + ∠DCB = 180

             3∠B + 2∠DCB + ∠DCB = 180°

                3∠B + 3∠DCB = 180°

                       3 ( ∠B + ∠DCB ) = 180

                               ∠B + ∠DCB = 180/3

                                ∠B + ∠DCB = 60

∴ Answer ; (A) 60°

Answer 2

Angle A=AngleB/2
Angle B= A/2
Angle ACD=2AngleDCB
DCB=ACD/2
A+D+C=180 angle sum property of triangle
angle D = angle DCB + angle B (by exterior angle property).
A+D+C=180
A+ANGLE DCB +B+C=180
A+C/2+A/2+C=180
3A+3C÷2=180
3(A+C)=360
A+C=120
A+C+D =180
D=60
angle DCB+AngleB=D=60
ANSWER=60