Question

in the figure AB ll CD , BE ll CF and angle ABD - 60° find the value of angle FCD .​

Answer 1

Answer:

Step-by-step explanatION

EXTEND LINE SEGMENT FE BACK SIDE IT INTERSECTES LINESEGMENT AB AT A POINT.

ANGLE CDE= ANGLE ABD (CORRESPONDING ANGLES)

ANGLE CDE= 60

ANGLE CDE+ ANGLE DCF = 180

60 +ANGLE FCD = 180

ANGLE FCD = 180-60

ANGLE FCD = 120 DEGREES

HOPE IT HELPS U

Answer 2

Question :-

In the figure AB | | CD , BE | | CF and ∠ABD = 60° . Find the value of ∠FCD

Answer :-

Given :-

AB || CD

BE || CF

∠ABD = 60°

Required to find :-

• Value of ∠FCD ?

Solution :-

Given that :-

AB || CD

BE || CF

∠ABD = 60°

We need to find the value of ∠FCD

So,

Let take that ,

AB || CD

where , BD is a transversal .

So,

∠ABD + ∠BDC = 180°

This is because ,

The sum of 2 interior angles on the same side of the transversal is equal to 180°

But ,

∠ABD = 60°

Hence,

60° + ∠BDC = 180°

∠BDC = 180° - 60°

∠BDC = 120°

Similarly ,

∠BDC + ∠CDE = 180°

Reason :-

Because they form a linear pair . And we know the sum of an linear pair is supplementary .

But ,

∠BDC = 120°

So,

120° + ∠CDE = 180°

∠CDE = 180° - 120°

∠CDE = 60°

Now,

consider that ;

BE || CF

Where , CD is the transversal .

However we can write that ;

∠FCD + ∠CDE = 180°

Reason :-

The sum of 2 interior angles on the same side of the transversal is equal to 180°

But ,

∠CDE = 60°

Hence,

∠FCD + 60° = 180°

∠FCD = 180° - 60°

∠FCD = 120°

$\huge{\rm{\therefore{ \angle{FCD} = {120}^{\circ}}}}$

Verification :-

From the given :-

BE || CF

CD is a transversal .

From the Figure ,

We can conclude that :-

∠BDC = ∠FCD

Reason :-

Alternate interior angles are equal .

So,

∠BDC = ∠FCD = 120°

( The value of ∠FCD obtained by the whole calculation is correct )

✅ Hence verified