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Question
In the given figure, the value of x is ______.
Options
65°
80°
95°
120°
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Solution
In the given figure, the value of x is 120°.
Explanation:
In the given figure, we need to find the value of x
Here, according to the angle sum property of the triangle
In ΔABD
∠BAD + ∠DBA + ∠ADB = 180°
55° + ∠DBA + 25° = 180°
80 + ∠DBA = 180°
∠DBA = 180° - 80°
∠DBA = 100°
∠DBA = 100°
Also, ABC is a straight line. So, using the property, “angles forming a linear pair are supplementary”, we get,
∠DBA + ∠DBC = 180°
100 + ∠DBC = 180°
∠DBC = 180° - 100°
∠DBC = 80°
Further, using the property, “exterior angle of a triangle is equal to the sum of two opposite interior angles”, we get
ext. ∠DOC + ∠OBC + ∠OCB
x = 80°+ 40°
x = 120°
Thus, x = 120°
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