Question

Find the value of x in the figure and prove that AD||BC.​

Answer 1

Step-by-step explanation:

In ∆BOC,

angle OBC=50°

OB=OC. (radii of the circle)

therefore, angle OCB=OBC=50° (isosceles triangle property)

angle COB=180-(50+50). (angle sum property)

180-100=80°

x= 80°(vertically opposite angle)

OD=OA (radii of the circle)

angle ODA=OAD(isosceles triangle property)

Angle D+A+O=180°(angle sum property)

2D+80=180(D=A)

2D=180-80=100

D=100/2

D=50°

Angle ODA=OBC=50°

AD//BC (alternate interior angles are equal )