Question

In the adjoining figure AB = 10cm, BC = 15cm AD: DC = 2 : 3 then find ABC.​

Answer 1

Step-by-step explanation:

Given ∆ABC in which AB=10,BC=15.AD:DC=2:3.

In ∆BDC angle BDC=130°, angle BCD=30° => angleCBD=20° .

Note AB/BC=10/15=2/3=AD/DC.

Hence BD is bisector of angle ABC.

Angle ABC=2angleCBD =2*20°=40°.

Hope this works.........

Answer 2

Answer:

Correct option is (B) 40°

Given:

AD/DC =2:3

AB=10 and BC=15

So, AB/BC=10/15=2/3

hece AB/BC=AD/DC=2/3

Thus, by converse of Angle Bisector theorem,

BD bisects ∠ABC

Now, In △BDC

Sum of angles = 180

∠BDC+∠DBC+∠BCD=180

130+30+∠DBC=180

∠DBC=20

∘

Since, DB bisecs ∠B

Hence, ∠B=2∠DBC=2×20=40°