12. Find the measure of \angle Pand \angle S if \overline {SP} || \overline {RQ} in Fig 3.34.
(If you find m\angle R, is there more than one method to find m\angle P?)

    

Answers (1)

Given,   \overline {SP} || \overline {RQ}

           \angle P+\angle Q=180\degree        (angles on same side of transversal)

             \angle P=180\degree-130\degree

             \angle P=50\degree

\angle R+\angle S=180\degree                    (angles on same side of transversal)

\angle S=180\degree-90\degree

\angle S=90\degree

Yes, to find m\angle P there is more than one method. 

PQRS is quadrilateral so sum of all angles is 360

\angle P+\angle Q+\angle R+\angle S=360\degree

and we know \angle Q,\:\angle R ,\:\angle S

so put valuse of  \angle Q,\:\angle R ,\:\angle S and we get measurement of \angle P

 

 

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