Question

Compute the value of x in the following figure:

Answer 1

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°