Question

DA=DB=DC , AB bisects angle ABC and angle ADB=60° find of x​

Answer 1

Answer:

From the figure

DA = DB = DC

Here BD bisects ∠ABC and ∠ADB=70

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In a triangle

∠ADB+∠DAB+∠DBA=180

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Substituting the values

70

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+∠DBA+∠DBA=180

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By further calculation

70

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+2∠DBA=180

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2∠DBA=180−70=110

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∠DBA=110/2=55

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Here BD is the bisector of ∠ABC

So ∠DBA=∠DBC=55

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In Δ DBC

DB = DC

∠DCB=∠DBC

Hence, x=55

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.ere PB is the bisector of ∠ABC

∠PBC=∠PBA

∠APB=∠PBC are alternate angles

x=∠PBC ….. (1)

In Δ ABC

∠A=60

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Since AB = AC we get ∠B=∠C

In a triangle

∠A+∠B+∠C=180

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Substituting the values

60∠+∠B+∠C=180∠

We get

60∠+∠B+∠B=180∠

By further calculation

2∠B=180−60=120

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∠B=120/2=60

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2

1

∠B=60/2=30

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∠PBC=30

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So from figure x=30

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