In the figure given below let’s write the measurement of ∠A + ∠B + ∠C + ∠D + ∠E + ∠F

Given: from the given figure AB||CF

To find the measurement of ∠A + ∠B + ∠C + ∠D + ∠E + ∠F

Now in the given figure, AB is parallel to CF with AD as tranversal line, so

∠A = ∠COD……….(i) (as they form is corresponding angles)

Similarly, AB is parallel to CF with BE as tranversal line, so

∠B = ∠FOE……….(ii) (as they form is corresponding angles)

Now consider ΔCOD,

We know in a triangle the sum of all three interior angles is equal to 180°.

So in this case,

∠C + ∠D + ∠COD = 180°

Substituting the values from equation(i), we get

∠C + ∠D + ∠A = 180°……..(iii)

Now consider ΔFOE,

We know in a triangle the sum of all three interior angles is equal to 180°.

So in this case,

∠E + ∠F + ∠FOE = 180°

Substituting the values from equation(ii), we get

∠E + ∠F + ∠B = 180°……..(iv)

Now adding equation (iii) and equation (iv), we get

∠A + ∠B + ∠C + ∠D + ∠E + ∠F = 180° + 180° = 360°

So the measurement of ∠A + ∠B + ∠C + ∠D + ∠E + ∠F = 360°.