Question

In the following figure, if ∠DAB = 60º, ∠ABD = 50º, then ∠ACB is equal to ______.

विकल्प

• 60º

• 50º

• 70º

• 80º

Answer 1

In the following figure, if ∠DAB = 60º, ∠ABD = 50º, then ∠ACB is equal to 70º.

Explanation:

Given: ∠DAB = 60°, ∠ABD = 50°

Using the theorem “angles in the same segment of the circle are equal”:

∴ ∠ADB = ∠ACB  ...(i)

In triangle ABD, using the angle sum property of triangle, we have:

∠ABD + ∠ADB + ∠DAB = 180°

⇒ 50° + ∠ADB + 60° = 180°

⇒ ∠ADB = 180° – 50° – 60°

⇒ ∠ADB = 70°

From equation (i), we have:

∴ ∠ACB = 70°