(Q15) Explain why the triangles are similar and then find the value of x.

vi)

12ABYZXX187.5

Solution :

Given : In △XYZ and △XBA,

∠X = ∠X [∵ Common]

∠B = ∠Y [∵ Pair of corresponding ∠A = ∠Z angles for AB ∥ ZY]

∴ △XYZ ~ △XBA [∵ AAA similarity]

Hence,
XY
XB
 =
YZ
BA
 =
XZ
XA
=
7.5 + x
x

[From the figure, XZ = 7.5 + x]

 =
7.5 + x
x

3x = + 2x;

3x - 2x =

x =