Question -
Answer -
In the given problem, we need to find the value of x
(i) In the given ΔABC, 
and 
Now, BCD is a straight line. So, using theproperty, “the angles forming a linear pair are supplementary”, we get,
Similarly, EAC is a straight line. So, we get,
Further, using the angle sum property of a triangle,
In ΔABC
Therefore, 
(ii) In the given ΔABC, 
and 
Here, BCD is a straight line. So, using theproperty, “the angles forming a linear pair are supplementary” we get,
Similarly, EBC is a straight line. So, we get
Further, using the angle sum property of a triangle,
In ΔABC
Therefore, 
(iii) In the given figure,
and 
Here,
and AD is thetransversal, so 
form a pair of alternate interiorangles. Therefore, using the property, “alternate interior angles are equal”,we get,
Further, applying angle sum property of the triangle
In ΔDEC
Therefore, 
(iv) In the given figure,
,
and 
Here, we will produce AD to meet BC at E
Now, using angle sum property of the triangle
In ΔAEB
Further, BEC is a straight line. So, using theproperty, “the angles forming a linear pair are supplementary”, we get,
Also, using the property, “an exterior angle of a triangle isequal to the sum of its two opposite interior angles”
In ΔDEC, x is its exterior angle
Thus,
Therefore,
.