Question

In the given figure, ΔODC ~ ΔOBA. If ∠BOC = 110°, ∠ODC = 45° and AB = 2CD, then find (i) m∠OAB (ii) OB : OD.

Answer 1

Given, ∠BOC = 110°, ∠ODC = 45° and AB = 2CD

(i) To find m∠OAB

∵ ΔODC ~ ΔOBA

So, ∠D = ∠B

45° = ∠B

Now, In ΔOAB,

∠1 + ∠A + ∠B = 180°

70° + ∠A + 45° = 180°

2A = 180° – 115°

∠A = 65°

(ii) OB : OD

∵ ΔODC ~ ΔOBA

`(OD)/(OB) = (DC)/(BA) = (OC)/(OA)`

So, `(OD)/(OB) = (DC)/(BA)`

And `(OB)/(OD) = (BA)/(DC)`  ...(By reversing)

`(OB)/(OD) = (AB)/(CD)`

`(OB)/(OD) = 2/1`

OB : OD = 2 : 1