1. In Fig. 6.13, lines AB and CD intersect at O. If ∠AOC +∠BOE = 70° and ∠BOD = 40°, find ∠BOE and reflex ∠COE.
Given:∠BOD=40 ∘ Since AB and CD intersects, ∠AOC=∠BOD(vertically opposite angles) ∠AOC=40 ∘ Also,∠AOC+∠BOE=70 ∘ ⇒∠BOE=70 ∘ −∠AOC=70 ∘ −40 ∘ =30 ∘ We need to find reflex∠COE Reflex∠COE=360 ∘ −∠COE Now, ∠AOC+∠COE+∠BOE=180 ∘ ⇒∠COE+(∠AOC+∠BOE)=180 ∘ ⇒∠COE+(40 ∘ +30 ∘ )=180 ∘ ⇒∠COE=180 ∘ −70 ∘ =110 ∘ Reflex∠COE=360 ∘ −110 ∘ =250 ∘
