Question

Compute the value of x in each of the following figures:

(i)

(ii)

(iii)

Answer 1

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 the property, “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 the property, “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 the transversal, so form a pair of alternate interior angles. Therefore, using the property, “alternate interior angles are equal”, we get,

Further, applying angle sum property of the triangle

In ΔDEC

Therefore,