Question

AB is a diameter and m∠ABC = 40°.
Find m∠CDB

Answer 1

Given:

m∠ABC = 40°

To find:

m∠CDB

Solution:

We have given the AB as the diameter of the circle.

And we know that the angle formed by the diameter of the circle at the boundary of the circle is a right angle.

So

m∠ACB = 90°

In ΔABC

By the angle sum property of the triangle:

∠CAB+∠ACB+∠CBA = 180°

∠CAB + 90° + 40° = 180°

∠CAB = 50°

From the property of the circle, the angle formed by the chord is same at all the points on the boundary of the circle.

So,

m∠CDB = 50°