Question

In the given figure, AD is a diameter. O is the centre of the circle. AD is parallel to BC and angle CBD =32°.

Answer 1

Here you go .hope this explains it well

Answer 2

Answer:

∠BED=58°,  ∠AOB=64°, ∠OBD=32°

Step-by-step explanation:

Given AD is a diameter. O is the center of the circle. AD is parallel to BC and ∠CBD =32°. we have to find the measure of angles.

As AD||BC

⇒ ∠ADB=∠CBD=32°

By angle sum Property of triangle in ΔABD

∠OAB+∠ABD+∠ADB=180°

⇒ ∠OAB+90°+32°=180°

⇒ ∠OAB=58°

As OA=OB gives ∠ABO=∠OAB=58°

In ΔABO, ∠OAB+∠ABO+∠AOB=180°

             ⇒ 58°+58°+∠AOB=180°

             ⇒ ∠AOB=64°

As ∠ABD=∠ABO+∠OBD

⇒ 90°=58°+∠OBD ⇒ ∠OBD=32°

Also, ∠BED=∠BAO=58°  (Angles made by same chord)