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In the adjoining figure, x: y: z = 5: 4: 6. If XOY is a straight line, find the values of x, y and z. |
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Answer» From the figure it is given that x: y: z = 5: 4: 6 We can also write it as x + y + z = 5 + 4 + 6 = 15 It is given that XOY is a straight line So we know that x + y + z = 180o As we know the sum of ratio is 15 then we can write that the measure of x as 5 The sum of all the angles in a straight line is 180o So we get the measure of x as x = (5/15) × 180 On further calculation x = 60 As we know the sum of ratio is 15 then we can write that the measure of y as 4 The sum of all the angles in a straight line is 180o So we get the measure of y as y = (4/15) × 180 On further calculation y = 48 In order to find the value of z We know that x + y + z = 180o Substituting the values of x and y we get 60o + 48o + z = 180o On further calculation z = 180o – 60o – 48o By subtraction we get z = 72o Therefore, the values of x, y and z are 60o, 48o and 72o. |
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