Question

In the given figure, DBC = 118° and BCE = 92°.Then ,BAC equals .(i) 55° (ii) 60° (iii) 42° (iv) 30° ​

Answer 1

Answer:

On line AE

angle ACB + angle BCE = 180°

angle ACB + 92° = 180°

angle ACB = 180° - 92° = 88°

similarly,

angle ABC = 180° - 118° = 62°

In triangle ABC,

ABC + BAC + ACB = 180°

62° + BAC + 88° = 180°

BAC = 180° - 150° = 30° ANS.

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Answer 2

BCA + BCE = 180° (linear pair)

BCA + 92° = 180°

BCA = 180° - 92° = 88°

ABC + DBC = 180° (linear pair)

ABC + 118° = 180°

ABC = 180° - 118° = 62°

BAC + BCA + ABC = 180° (Angle sum property of triangle)

BAC + 88° + 62° = 180°

BAC + 150° = 180°

BAC = 180° - 150°

BAC = 30° (Ans)

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