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