In ∆PQR, QR is extended up to S, so that RS = RP. If ∠RPQ = 55° and ∠PRS = 110°, then find the measure of ∠PQS.

Correct option is A

Given:

- In $$\triangle PQR ,$$​side QR is extended to S such that RS = RP

$$- \angle RPQ = 55^\circ .\\ - \angle PRS = 110^\circ$$​​

Identity Used:

In a triangle, the sum of the angles is $$180^\circ$$​ . We also use the property that the exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Solution:

Since $$\angle PRS = 110^\circ$$​is an exterior angle to  $$\triangle PQR$$​ , we can write:

​$$\angle PRS = \angle RPQ + \angle PQS\\110^\circ = 55^\circ + \angle PQS$$​​

Solving for  $$\angle PQS :$$​​

​$$\angle PQS = 110^\circ - 55^\circ = 55^\circ$$​​

Therefore, the measure of $$\angle PQS$$​ is 55°.