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Question
In the following figure, if ∠DAB = 60º, ∠ABD = 50º, then ∠ACB is equal to ______.
Options
60º
50º
70º
80º
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Solution
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°
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