Answer:
x=16
Step-by-step explanation:
We are given a ΔAGL.
E and N are the points on line AL and AG respectively.
Refer the figure
We can see that EN = 21 and LG = 42
⇒ EN is half of LG and we can see that EN is parallel to LG
So, mid segment theorem states that the segment passing through the midpoints of two sides of triangle and parallel to third side then it is also half of the third side.
So, Since EN is half of LG and we can see that EN is parallel to LG
So, E is the mid point of AL i.e. AE =AL and N is the midpoint of AG i.e.
AN = NG
Now since AN = NG
And we can see that AN =2x-9
And NG = x+7
⇒2x-9 = x+7
⇒2x-x = 7+9
⇒x = 16
Thus the value of x is 16
