Question

A, B & C lie on a straight line. BD = CD. ∠ BDC = 30° and ∠ ADB = 30°. Work out x ,

Answer 1

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Answer 2

Given :- A, B & C lie on a straight line. BD = CD. ∠ BDC = 30° and ∠ ADB = 30°. Work out x ?

Solution :-

In ∆DBC we have,

→ DB = DC (given)

so,

→ ∠DBC = ∠DCB (Angle opposite to equal sides are equal.)

and,

→ ∠BDC = 30° (given)

then,

→ ∠DBC + ∠DCB + ∠BDC = 180° (By angle sum property.)

→ 2∠DBC + 30° = 180°

→ 2∠DBC = 180° - 30°

→ ∠DBC = 150°/2

→ ∠DBC = 75°

now, since AC is a straight line . so,

→ ∠DBC + ∠ABD = 180° (linear pair)

→ ∠ABD = 180° - 75°

→ ∠ABD = 105°

now, in ∆ABD we have,

→ ∠ADB = 30° (given)

→ ∠BAD = x

therefore,

→ ∠ABD + ∠BAD + ∠ADB = 180° (By angle sum property.)

→ 105° + x + 30° = 180°

→ 135° + x = 180°

→ x = 180° - 135°

→ x = 45° (Ans.)

Learn more :-

In ABC, AD is angle bisector,

angle BAC = 111 and AB+BD=AC find the value of angle ACB=?

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