Question

Find x in Figure Given: DA = DB = DC, BD bisects ∠ABC and∠ADB = 70°.

Answer 1

In the figure,

DA = DB = DC

BD bisects ∠ABC
and ∠ADB = 70°

But ∠ADB + ∠DAB + ∠DBA = 180° ............(Angles of a triangle)

⇒ 70° + ∠DBA + ∠DBA = 180° ........(∵ DA = DB)

⇒ 70° + 2 ∠DBA = 180°

⇒ 2 ∠DBA = 180° − 70°

= 110°

∴ ∠DBA =`(110°)/2=55°`

∵ BD is the bisector of ∠ABC,

∴ ∠DBA = ∠DBC = 55°

But in Δ DBC,

DB = DC

∴ ∠DCB = ∠DBC

⇒ x = 55°