If ∠ AOC + ∠ BOE = 70° and ∠ BOD = 40°, find ∠ BOE and reflex ∠ COE.
NCERT Class 9 Mathematics Chapter 6
Page No. 96
Exercise 6.1
Question No. 1
In Fig. 6.13, lines AB and CD intersect at O.
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Given: Lines AB and CD intersects at O such that ∠BOD = 40° and
∠AOC + ∠BOE = 70° …(1)
∠AOC = ∠BOD [∵ Vertically Opposite Angles]
Hence, ∠AOC = 40° [∵ ∠BOD = 40°]
Therefore, from the equation (1), we have,
40° + ∠BOE = 70°
⇒ ∠BOE = 70° – 40° = 30°
Here, ∠AOC + ∠BOE + ∠COE = 180° [∵ AOB is a straight line]
⇒ 70° + ∠COE = 180° [From the equation (1)]
⇒ ∠COE = 180° – 70° = 110° and
Relex ∠COE = 360° – ∠COE = 360° – 110° = 250°