Q4 of 153 Page 118

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°


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