Question

Please sove this question.

Answer 1

Step-by-step explanation:

Since EF || CD,

angle FEC and angle ECD are Co interior angles. So, they are supplementary.

So,

angle FEC + angle ECD = 180°. That is,

165° + ECD = 180°. So,

ECD = 180° - 165° = 15°.

Now,

angle BCD = angle BCE + angle ECD. That is,

BCD = 25° + 15° = 40°.

Now,

Consider lines, AB and CD, cut by transversal, BC.

Here,

angle ABC and angle BCD are alternate interior angles.

Given, ABC = 40°.

So, we find that,

angle ABC = angle BCD = 40°.

This happens only if AB and CD are parallel.

So,

AB || CD. Hence, proved.

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