Question

34. In triangle ABC, DE || BC, ADE= 70° and BAC = 50°, then BCA = = (a) 60° (b) 70° (C) 50° (d) 120°...

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Answer 1

Answer:

a) 60°

Step-by-step explanation:

Given that in ∆ABC, DE || BC, angle ADE is 70° and angle BAC is 50°. We need to find out the angle BCA.

(Refer the attachment for figure.)

As said that DE || BC. So, angle ADE is equal to angle ABC.

→ ∠ADE = ∠ABC

and ∠ADE = 70°

Therefore,

→ ∠ABC = 70°

And we know that sum of all angles of triangle is 180°. So, in ∆ABC

→ ∠ABC + ∠BCA + ∠BAC = 180°

→ 70° + ∠BCA + 50° = 180°

→ 120° + ∠BCA = 180°

→ ∠BCA = 180° - 120°

→ ∠BCA = 60°

Hence, ∠BCA is 60°.