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Set the middle point as O.

Within triangle PON, ∠b + ∠c = 180º – ∠PON
Within triangle QOS, ∠e + ∠d = 180º – ∠QOS
Therefore, ∠b + ∠c + ∠e + ∠d = 180º x 2 – (∠PON + ∠QOS)

∠PON + ∠QOS + ∠SON = 180º

Hence, ∠b + ∠c + ∠e + ∠d = 180º x 2 – 180º + ∠SON = 180º + ∠SON

∠SON = ∠ROM

∠b + ∠c + ∠e + ∠d = 180º + ∠SON

∠a + ∠b + ∠c + ∠e + ∠d = 180º + ∠SON + ∠a

∠SON +∠ a = 180 – ∠MRO = 180º – 80º = 100º

Hence, ∠a + ∠b + ∠c + ∠e + ∠d = 180º + 100º = 280º

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