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

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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°