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Question
Compute the value of x in the following figure:
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Solution
In the given problem, we need to find the value of x
In the given ΔABC, ∠ACD = 110° and ∠EBA = 120°
Here, BCD is a straight line. So, using the property, “the angles forming a linear pair are supplementary” we get,
∠ACB + ∠ACD = 180°
∠ACB + 110° = 180°
∠ACB = 180° - 110°
∠ACB = 70°
Similarly, EBC is a straight line. So, we get
∠EBA + ∠ABC = 180°
120° + ∠ABC = 180°
∠ABC = 180° - 120°
∠ABC = 60° V
Further, using the angle sum property of a triangle,
In ΔABC
∠ACB + ∠BAC + ∠ABC = 180°
70° + 60° ∠BAC = 180°
130° + ∠BAC = 180°
∠BAC = 180° - 130°
∠BAC = 50°
Therefore, x = 50°
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