Question

In Fig. ABCD is a rectangle in which diagonal AC is produced to E. If ∠ECD =146°, find ∠AOB.

Answer 1

Given, 

ABCD is a rectangle 

∠ECD = 146° 

= ∠ECD +∠DCO = 180° 

(Linear pair of angles)

=146°+∠DCO = 180° 

= ∠DCO = 180° - 146° = 34° 

And, 

∠BOC = 180°- ∠OCB -∠OBC 

∵ ∠OCB = ∠OBC 

=∠BOC = 180°- 34°- 34° = 112° 

∠BOC +∠AOB = 180° 

(Linear pair) 

= 112°+ ∠AOB = 180° 

= ∠AOB = 180°- 112° = 68°