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