Question

2. In the given figures AB || CD || EF, calculate x.
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Answer 1

Answer:

It is given that AB || CD and BC is a transversal From the figure we know that ∠BCD and ∠ABC are alternate interior angles So we get ∠ABC = ∠BCD In order to find the value of x we can write it as xo + ∠ECD = 70o ……. (1) It is given that CD || EF and CE is a transversal From the figure we know that ∠ECD and ∠CEF are consecutive interior angles So we get ∠ECD + ∠CEF = 180o By substituting the values ∠ECD + 130o = 180o On further calculation we get ∠ECD = 180o – 130o By subtraction ∠ECD = 50o Now by substituting ∠ECD in equation (1) we get xo + ∠ECD = 70o xo + 50o = 70o On further calculation we get xo = 70o – 50o By subtraction xo = 20o Therefore, the value of x is 20.

Answer 2

a) make an imaginary line passing through O which splits angle x into 2 angles,then suppose one angle a and another b(don't write this in your copy make these changes in the figure)

here,

a=60°[being alternate angle]

b=80°[being alternate angle]

now,

a+b=x[being two angles which is a part of the angle 'x']

or,x=60°+80°

∴ x=140°