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Question

In the adjoining figure, AB = 10 cm, BC =15 cm AD : DC = 2 : 3, then \(\angle\)ABC is equal to -


A

30

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B

40

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C

45

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D

110

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Solution

The correct option is B

40


Clearly, ADDC = 23 and ABBC = 1015 = 23

So, ADDC = ABBC

Thus, BD divides AC in the ratio of the other two sides.

By Converse of Angular Bisector theorem,
BD is the bisector of B
ABC = 2 ( CBD)

Now, CBD = 180 - (130 + 30) .... (Angle Sum Property)
= 20

But , ABC = 2 ( CBD)
= 2 x 20
= 40


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