Question

In the figure, angleABD=3 angle DAB and angle BDC=96 .find angle ABD​

Answer 1

In △ABC

∠ABD=3∠DAB (given)

and ∠BDC=96

∘

∠BDC+∠BDA=180

∘

(linear pair)

⇒96

∘

+∠BDA=180

∘

⇒∠BDA=180

∘

−96

∘

=84

∘

In △ABD,∠ABD+∠DAB+∠BDA=180

∘

(angle sum property)

⇒3∠DAB+∠DAB+84

∘

=180

∘

⇒4∠DAB=180

∘

−84

∘

=96

∘

⇒∠DAB=

4

96

∘

=24

∘

and ∠ABD=3∠DAB=3×24

∘

=72

∘

Answer 2

Please refer to the following attachment

Thanks