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Question
In the given figure, if AB ⊥ BC. then x =
Options
18
22
25
32
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Solution
In the given figure, AB ⊥ BC
We need to find the value of x.
Now, since AB and CD are straight lines intersecting at point O, using the property, “vertically opposite angles are equal”, we get,
∠BOC = ∠AOD
∠BOC = 32°
Further, applying angle sum property of the triangle
In ΔBOC
∠BOC + ∠OBC + ∠BCO = 180°
32° + 90° + ∠BCO = 180°
∠BCO = 180° -122°
∠BCO = 58°
Then, using the property, “an exterior angle of the triangle is equal to the sum of the two opposite interior angles”, we get,
In ΔEOC
∠BCO = ∠OEC +∠EOC
58° = (x + 14)° + x
58° = 2x + 14°
2x = 58° - 14°
Further solving for x, we get,
2x = 44°
`x = (44° )/2`
x = 22°
Thus x = 22°
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