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Question -

The exterior angles, obtained on producing the base of a triangle both way are 104° and 136°. Find all the angles of the triangle.



Answer -

In the given problem, the exterior angles obtained on producing the base of a triangle both ways are  and  . So, let us draw ΔABC and extend the base BC, such that:

Here, we need to find all the three angles of the triangle.
Now, since BCD is a straight line, using the property, “angles forming a linear pair are supplementary”, we get
Similarly, EBC is a straight line, so we get,
Further, using angle sum property in ΔABC
Therefore,

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