Question

Find each angle shown in the diagram.

Answer 1

In the figure,

${\displaystyle 3\frac{1}{2}\text{y}°+2\text{y}°+2\text{y}°+2\frac{1}{2}\text{y}°=360°}$ .........(Angles at a point)

⇒ ${\displaystyle \frac{7}{2}\text{y}°+2\text{y}°+2\text{y}°+\frac{5}{2}\text{y}°=360°}$

⇒ ${\displaystyle \frac{7}{2}\text{y}°+\frac{5}{2}\text{y}°+4\text{y}°=360°}$

⇒ ${\displaystyle \frac{12}{2}\text{y}°+4\text{y}°=360°}$

⇒ 6y° + 4y° = 360°

⇒ 10y° = 360°

⇒ y = ${\displaystyle \frac{360°}{10}}$ = 36°

∴ ∠AOB = ${\displaystyle 3\frac{1}{2}\text{y}°=\frac{7}{2}\text{y}°=\frac{7}{2}\times 36°}$
= 126°

∠BOC = 2y° = 2 × 36° = 72°

∠COD = 2y° = 72°

∠DOA = ${\displaystyle 2\frac{1}{2}\text{y}°=\frac{5}{2}\text{y}°}$
= ${\displaystyle \frac{5}{2}\times 36°}$ = 90°