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प्रश्न
In the given figure, compute the value of x.
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उत्तर
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°.
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