Question

pQRS and LMNQ are parellelgrams lf angleQ=60°,find angle L,angle M,angleP,angleS and angleR​

Answer 1

Proved below.    

Step-by-step explanation:

Given:

Here PQRS is a parallelogram and ∠ SPQ = 60°

And ∠ P + ∠ Q = 180° ⇒∠ Q = 120°.  (sum of interior angles on the same side of transversal)  

AP is the angle bisector  

∴ ∠SPA = ∠APQ = 30°                (1)

Similarly, ∠AQR = ∠AQP = 60°

PQ is parallel to SR and PA is a transversal  

∴∠SAP = ∠APQ = 30°   (alternate angles)

∴∠SAP = ∠SPA   (from 1)

Now in ΔPAS,  

∠SAP = ∠SPA  

∴ SA = PS               (by isosceles triangle property)          (2)

Similarly AR=RQ                                                                    (3)

also PS = RQ           (sides of parallelogram)                      (4)

By (2), (3) and (4)

SA = AR

∴ A is the mid point of SR.

Hence proved