Question

In the adjoining figure,<B=70° and <A =50°. If the bisector of <C meets AB in D, then find <ADC.​

Answer 1

Answer:

ABC

∠A+∠B+∠C=180

50

∘

+70+∠C=180

120

∘

+∠C=180

∠C=180

∘

−120

∘

=60

∘

Since CD is the bisector ∠C

So, ∠ACD=∠BCD=

2

∠C

=

2

60

∘

=30

∘

In triangle ADC

∠ACD+∠DAC+∠ADC=180

∘

30

∘

+50

∘

+∠ADC=180

∘

∠ADC=180

∘

−80

∘

∠ADC=100

∘

∠ADC+∠BDC=180

∘

100

∘

+∠BDC=180

∘

∠BDC=180

∘

−100

∘

∠BDC=80

∘

So in triangle ADC

∠DAC=50

∘

,∠ACD=30

∘

,∠ADC=100

∘

In triangle BDC

∠DBC=70

∘

,∠BCD=30

∘

,∠BDC=80

∘

And ∠BDC=80

∘

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Answer 2

Answer:

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