Question

Find each angle shown in the diagram.

Answer 1

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°