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Similarity of Triangles CBSE NCERT Solutions Chapter 6 Triangles Exercise 6.3 Question 2

CBSE NCERT Solutions Chapter 6 Triangles Exercise 6.3 Question 2

 

2.   In fig 6.35, \triangle ODC ~ \triangle OBA, \angle BOC = 125^\circ and \angle CDO = 70^\circ. Find \angle DOC, \angle DCO and \angle OAB.


Similarity of Triangles Sample Problem
Fig 6.35

 

 

Solution:

 

Given: \triangle ODC ~ \triangle OBA, \angle BOC = 125^\circ and \angle CDO = 70^\circ

 

\angle BOC\angle DOC = 180^\circ    {Linear Pair}

\Rightarrow \angle DOC = 180 - 125 = 55^\circ

 

In \triangle ODC

 

\angle ODC\angle DCO\angle COD = 180^\circ   {Sum of angles of Triangle}

 

\Rightarrow 70 + 55 + \angle DCO = 180

 

\Rightarrow \angle DCO = 180 - 70 - 55 = 55^\circ

 

 

It is given that \triangle ODC ~ \triangle OBA.

 

Therefore, corresponding angles of \triangle ODC and \triangle OBA are equal.

 

By, AAA similarity criterion, \angle OCD = \angle OAB

 

Therefore, \angle OAB = 55^\circ



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