Q. 94.7( 25 Votes )
In the given figure, AB||CD. Prove that p+q-r=180

Answer :
Given AB||CD, ∠AEF = P°, ∠EFG = q°, ∠FGD = r°
Draw a line FH||AB||CD
∠HFG = ∠FGD = r° [Because HF||CD and alternate angles] ___________ (i)
∠EFH = ∠EFG - ∠HFG
⇒ ∠EFH = q – r ______________________ (i)
∠AEF + ∠EFH = 180° [Because AB||HF]
⇒ ∠AEF + ∠EFH = 180°
⇒ p + (q – r) = 180°
⇒ p + q – r = 180°Proved.
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