Question

. In the following figure, find the value of x.​

Answer 1

Answer:

X = 90°

Step-by-step explanation:

First name the ∠EBA as ∠1 and ∠CBD = ∠2

∠1 + 80° +70° = 180°(Angle Sum Property)

⇒∠1  + 150° = 180°

⇒∠1  =  180° - 150°

⇒∠1  = 30°

∠1 =∠2 ( Vertically opposite Angles)

So ∠2 = 30°

∠2 + x + 60° = 180°( Angle Sum property)

⇒30° + x + 60° = 180°

⇒90° +x = 180°

⇒x = 180° -90°

⇒x = 90°

Hope this will help you

Answer 2

Answer:

In triangle AEB,

∠BEA + ∠BAE + ∠ABE = 180°

[ Angle Sum Property of Triangle ]

=> 80° + 70° + ∠ABE = 180°

=> 150° + ∠ABE = 180°

=> ∠ABE = 180° - 150°

=> ∠ABE = 30°

Now, ∠ABE = ∠DBC = 30°

[ Vertically Opposite Angles ]

Finally, in triangle DBC

∠BCD + ∠DBC + ∠BDC = 180°

[ Angle Sum Property of Triangle ]

=> 60° + 30° + ∠BDC = 180°

=> 90° + ∠BDC = 180°

=> ∠BDC = 180° - 90°

=> ∠BDC = 90°

Therefore, ∠BDC = ∠x = 90°

Hope it helped you..

Thank you !!!