Question

In the given fig. DE || BC, ∟ADE =70° and ∟BAC=50°, then angle ∟BCA = ______
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Answer 1

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Answer 2

∠BCA = 60°

GIVEN

ABC is a ∆

DE || BE

∠BAC = 50°

∠ADE = 70°

TO FIND

∠BCA

SOLUTION

We can simply solve the above problem as follows-

Since,

DE || BE

So, According to corresponding angle theoram,

∠ADE = ∠ABC = 70°

Now,

In ΔABC

We know that sum of all the angles of a triangle is 180°

So,

∠BAC + ∠ABC + ∠ACB = 180°

50 + 70 + ∠ACB = 180°

120° + ∠ACB = 180

∠ACB = 180-120 = 60°

Hence, ∠BCA = 60°

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