In $$\triangle PQR$$, QR is extended up to S, so that RS = RP, If $$\angle RPQ$$ = $$55^o$$ and $$\angle PRS$$ = $$110^o$$, then find the measure of $$\angle PQS$$.​

△PQR, where QR is extended to S, and RS = RP

Concept Used:
The external angle is equal to the sum of the two opposite interior angles.

Solution:   

From the property of the external angle triangle;

​$$\angle PRS = \angle QPR + \angle PQR \\ \ \\ 110\degree = 55\degree + \angle PQR \\ \ \\ \angle PQR = 110 - 55 = 55\degree$$ 

we know that,

​$$\angle PQR = \angle PQS$$​​

Thus,  $$\angle PQS = \bf 55\degree$$​​