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Question
Side BC of a triangle ABC has been produced to a point D such that ∠ACD = 120°. If ∠B = \[\frac{1}{2}\]∠A is equal to
Options
80°
75°
60°
90°
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Solution
In the given problem, side BC of ΔABC has been produced to a point D. Such that ∠ACD = 120° and `∠B = 1/2 ∠A` . Here, we need to find ∠A
Given `∠B = 1/2 ∠A`
We get, ∠A = 2∠B .........(1)
Now, using the property, “exterior angle of a triangle is equal to the sum of two opposite interior angles”, we get,
In ΔABC
∠ACD = ∠A + ∠B
120° = 2∠B + ∠B
120° = 3∠B
`∠B = (120°)/3`
∠B = 40°
Also, ∠A = 2∠B(Using 1)
∠ A = 2 (40°)
= 80°
Thus, ∠A = 80°
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