Question

in the given figure, AB || CD , find the value of x,y and z if angle AEF = 75° ,angle EGD= 125° , angle FEG= z° , angle CFE= x° , angle EFG= y°​

Answer 1

Answer:

It is given that AB || CD and EF is a transversal From the figure we know that ∠AEF and ∠EFG are alternate angles So we get ∠AEF = ∠EFG = 75o ∠EFG = y = 75o From the figure we know that ∠EFC and ∠EFG form a linear pair of angles So we get ∠EFC + ∠EFG = 180o It can also be written as x + y = 180o By substituting the value of y we get x + 75o = 180o On further calculation we get x = 180o – 75o By subtraction x = 105o From the figure based on the exterior angle property it can be written as ∠EGD = ∠EFG + ∠FEG By substituting the values in the above equation we get 125o = y + z 125o = 75o + z On further calculation we get z = 125o – 75o By subtraction z = 50o Therefore, the values of x, y and z are 105o, 75o and 50°

Step-by-step explanation:

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