Question

If if ab parallel angle abc is equal to 115 degree and Angle b is equal to 125 degree then angle BCD is what answer them

Answer 1

Answer:

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Question

If AB || DE, ∠ABC = 115° and ∠CDE = 110°, find ∠BCD.

F1 Amar.T 01-07-21 Savita D14

35°

45°

40°

30°

Answer (Detailed Solution Below)

Option 2 : 45°

Detailed Solution

Given:

∠ABC = 115° and ∠CDE = 110°

Concept used:

We can use the properties of angles formed between parallel lines to find the value of ∠BCD.

By extending the lines as depicted in the figure, where MN is parallel to the line AB and DE.

Construction:

Prduce CB to F and draw a line MN || AB || DE passes through C.

Calculation:

F1 Amar.T 01-07-21 Savita D15

∠ABF = 180 - 115 [By linear pair of angles]

⇒ ∠ABF = 65°

∠FCM = ∠ABF = 65° [Corresponding angles]

∠DCN = 180 - 110 [Angles on the same side of transversal]

∠DCN = 70°

According to the figure, we have

∠MCB + ∠BCD + ∠DCN = 180°

⇒ 65° + ∠BCD + 70° = 180°

⇒ ∠BCD = 180 - 135

⇒ BCD = 45°

∴ The value of ∠BCD is 45°