Question

In the given figure, compute the value of x.

Answer 1

In the given figure,∠DCB = 45, ∠CBA = 45 and ∠BAD = 35

Here, we will produce AD to meet BC at E

Now, using angle sum property of the triangle

In ΔAEB

∠BAE +∠AEB + ∠EBA = 180°

∠AED + 35°+ 45° = 180°

∠AEB + 80° = 180°

∠AEB = 180° - 80°

∠AEB = 100°

Further, BEC is a straight line. So, using the property, “the angles forming a linear pair are supplementary”, we get,

∠AEB + ∠AEC = 180°

100 + ∠AEC = 180°

∠AEC = 180°- 100°

∠AEC = 80°

Also, using the property, “an exterior angle of a triangle is equal to the sum of its two opposite interior angles”

In ΔDEC, x is its exterior angle

Thus,

∠X = ∠DCE + ∠DEC

= 50° + 80°

= 130°
Therefore, X = 130°.