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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 = 112° and ∠BAE = 120°
Now, BCD is a straight line. So, using the property, “the angles forming a linear pair are supplementary”, we get,
∠ABC + ∠ACD = 180°
∠ABC + 112 = 180°
∠ACB = 180° - 112°
∠ACB = 68°
Similarly, EAC is a straight line. So, we get,
∠BAE + ∠BAC = 180°
120° + ∠BAC = 180°
∠BAC = 180° - 120°
∠BAC = 60°
Further, using the angle sum property of a triangle,
In ΔABC
∠ACB + ∠BAC + ∠ABC = 180°
68° + 60° + ∠ABC = 180°
128° + ∠ABC = 180° -128°
∠ABC = 52°
Therefore, x = 52°
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