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Question
Find each angle shown in the diagram.
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Solution
In the figure,
`3 1/2"y"°+2"y"°+2"y"°+2 1/2"y"°=360°` .........(Angles at a point)
⇒ `7/2"y"°+2"y"°+2"y"°+5/2"y"°=360°`
⇒ `7/2"y"°+5/2"y"°+4"y"°=360°`
⇒ `12/2"y"°+4"y"°=360°`
⇒ 6y° + 4y° = 360°
⇒ 10y° = 360°
⇒ y = `(360°)/10` = 36°
∴ ∠AOB = `3 1/2"y"°=7/2"y"°=7/2xx36°`
= 126°
∠BOC = 2y° = 2 × 36° = 72°
∠COD = 2y° = 72°
∠DOA = `2 1/2"y"°=5/2"y"°`
= `5/2xx36°` = 90°
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