question_answer 25)

                Find the measure of \[\angle P\] and \[\angle S\]. If \[\overline{SP}||\overline{RQ}\] in the figure. (If you find \[m\angle R,\] there more than one method to find \[m\angle P\]?)

Answer:

\[\because \]     \[SP||RQ\] \[\therefore \]  \[m\angle P+m\angle Q={{180}^{\text{o}}}\] |i.e., the sum of interior opposite angles is \[{{180}^{\text{o}}}\] \[\Rightarrow \]               \[m\angle P+{{130}^{\text{o}}}={{180}^{\text{o}}}\] \[\Rightarrow \]               \[m\angle P={{180}^{\text{o}}}-{{130}^{\text{o}}}\] \[\Rightarrow \]               \[m\angle P={{50}^{\text{o}}}\] \[m\angle R={{90}^{\text{o}}}\]