(Q11) Explain why the triangles are similar and then find the value of x.

ii)

Solution :

Given : In △ABC and △PQC

∠B = ∠Q

[∵ ∠PQC = 180°- 110° = 70° - linear pair of angles]

∠C = ∠C [∵ Common]

∠A = ∠P [∵ Angle Sum property of triangles]

△ABC ~ △PQC by AAA similarity condition.

Then the ratio of their corresponding sides are equal.