In the adjoining figure, x: y: z =5:4:6. If XOY is a straight line, find the values of x, y and z
X=60, Y=48, Z=72
AOB is a straight line
Therefore, ∠XOP + ∠POQ + ∠YOQ = 180°
Given, x: y: z =5: 4: 6
Let ∠XOP = x° = 5a, ∠POQ = y° = 4a, ∠YOQ = z° = 6a
⇒ 5a + 4a + 6a = 180°
⇒ 15a = 180°
⇒ a = 12°
Therefore,
x = 5a = 5×12° = 60°
y = 4a = 4×12° = 48°
z = 6a = 6×12° = 72°