Ncert solutions

# Question 12

Q12) Find the measure of \angle P\ and\ \angle S\ if\ \overline{SP}\parallel\overline{RQ} in given figure.

(If you find m\angle R is there more than one method to find m\angle P)

Solution:

Here, \angle P+\angle Q=180\degree

[Sum of co-interior angles is 180\degree]

\Rightarrow\angle p+130\degree=180\degree

\Rightarrow\angle p=180\degree-130\degree

\Rightarrow\angle p=50\degree

\because\angle R=90\degree [Given]

\therefore\angle S+90\degree=180\degree

\Rightarrow\angle S=180\degree-90\degree

\Rightarrow\angle S=90\degree

Yes, one more method is there to find \angle p.

\Rightarrow90\degree+90\degree+130\degree+\angle p=360\degree

\Rightarrow310\degree+\angle p=360\degree

\Rightarrow\angle p=360\degree-310\degree

\Rightarrow\angle p=50\degree

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