Question

11
From the figure, find x of AB || CD.

(A) 45°
(B) 55°
(C) 60°
(D) 70°​

Answer 1

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✿ Required Answer:

✒ GiveN:

• AB || CD || EF
• ∠BCE = 25°
• ∠CEF = 150°

✒ To FinD:

• Find ∠ABC(x)......?

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✿ How to solve?

For solving this questions, Let's know some conclusions regarding parallel line and a transversal that cuts them.

• If two parallel lines are cut by a transversal, then each pair of alternate interior angles are congruent.
• Each pair of consecutive interior angles on the same side of transversal is supplementary.
• Each pair of alternate exterior/Interior angles is congruent.
• Each pair of corresponding angles is congruent.

☃️ So, For these statements, we can use it in a way to find the value of x in above lines and angles diagram.

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✿ Solution:

We have,

• EF || CD
• ∠FEC = 150°

Then, ∠FEC and ∠CED are interior consecutive angles, hence they add upto 180°

➝ ∠FEC + ∠ECD = 180°

➝ 150° + ∠ECD = 180°

➝ ∠ECD = 30°...........(1)

And, also

• AB || CD
• ∠BCE = 25°

Here, ∠ABC and ∠BCD are alternate interior angles, hence they are congruent.

➝ ∠ABC = ∠BCD

➝ ∠ABC = ∠BCE + ∠ECD

➝ ∠ABC = 25° + 30° [∠ECD from eq.(1)]

➝ ∠ABC = 55°

➝ x° = 55°

✒ Value of x in degrees = 55°.

⚘$\large{ \gray{ \underline{ \underline{ \bf{Option \: b}}}}}$

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Answer 2

Option b (55°)

Given :-

• AB || CD

To Find :-

• Value of "x".

Solution :-

=> ∠FEC + ∠ECD = 180° ( Linear Pair)

=> 150° + ∠ECD = 180°

=> ∠ECD = 180° - 150°

=> ∠ECD = 30°

AB || CD and BC is transversal,

=> ∠ABC = ∠BCD (Alternate angle)

=> .°. x = ∠BCD

=> ∠BCD = ∠BCE + ∠ECD

=> ∠BCD = 25° + 30°

=> ∠BCD = 55°

.°. x = 55° ( °.° x = ∠BCD )

Thus, The value of x is 55°.