Question

. In the given figure, AB || CD, ABF = 45°, then FDC is​

Answer 1

Answer:

<B =<C =45°(alternate interior angle)

In triangle FDC

<CFD=110°

<FCD=45°

So,

110+55+<FDC=180°

<FDC+155=180

<FDC=180-155

<FDC=25°

Answer 2

Given:

AB || CD, angle ABF = 45°, angle CFD = 110°.

To find:

The angle FDC.

Solution:

The measure of angle FDC is 25°.

To answer this question, we will follow the following steps:

As given in the question, we have,

AB is parallel to CD

angle ABF = 45°

angle CFD = 110°

Now,

As we know if two lines are parallel then the alternate interior angles formed by a transversal will be equal.

So,

angle ABF = angle FCD

As

angle ABF = 45°

So,

angle FCD = 45°

Now,

In triangle FCD,

angle CFD + angle FCD + angle FDC = 180° (sum property of interior angles of a triangle)

110° + 45° + angle FDC = 180°

155° + angle FDC = 180°

angle FDC = 180° - 155°

angle FDC = 25°

Hence, the measure of angle FDC is 25°.