Question

In the given figure, if AB ⊥ BC. then x =

पर्याय

• 18

• 22

• 25

• 32

Answer 1

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°