Question

DB is a diameter of circle O. If mACB = 30°, what is the mDBA?

30°

50°

60°

70°

90°

Answer 1

m∠ABD = 60°

Explanation:

Answer 2

m∠ABD = 60°

Explanation:

From the given figure :

Given : m∠ACB = 30°

To find : m∠DBA

Solution : Since, the angle formed in the same segment are equal in the circle

⇒ m∠ACB = m∠ADB

Since, m∠ACB = 30°

⇒ m∠ADB = 30°

Now, Angle formed in the semicircle is right angle

⇒ m∠BAD = 90°

So, by using angle sum property of a triangle in the ΔADB. We get,

m∠ADB + m∠ABD + m∠BAD = 180

⇒ 30 + m∠ABD + 90 = 180

⇒ m∠ABD + 120 = 180

⇒ m∠ABD = 60°