Need help with inscribed angles If M

Given:

In the given circle O, BC is diameter, OA is radius, DC is a chord parallel to chord BA and .

To find:

The .

Solution:

If a transversal line intersect two parallel lines, then the alternate interior angles are congruent.

We have, DC is parallel to BA and BC is the transversal line.

       [Alternate interior angles]

In triangle AOB, OA and OB are radii of the circle O. It means OA=OB and triangle AOB is an isosceles triangle.

The base angles of an isosceles triangle are congruent. So,

     [Base angles of an isosceles triangle]

Using the angle sum property in triangle AOB, we get

Hence, the measure of angle AOB is 120 degrees.

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