Q. Calculate the angles marked with small letters in the following diagram.

 

Dear student,
$$\begin{gathered} \angle SOR=\angle POQ =102° --[vert. opp. angles] \\ Since the diagonals of rec\tan gle are equal and bisects each other. \\ \therefore SO=OR \\ \Rightarrow \angle SRO=\angle RSO =b \\ Now, In ∆SOR, \\ \angle SRO+\angle RSO+\angle SOR=180° \\ \Rightarrow b+b+102°=180° \\ \Rightarrow 2b=180°-102° \\ \Rightarrow 2b=78° \\ \Rightarrow \boxed{b=39°} \\ Now, \angle SRQ=\angle SRO+\angle QRO \\ \Rightarrow 90°=b+a \\ \Rightarrow 90°=39°+a \\ \Rightarrow a=90°-39° \\ \Rightarrow \boxed{a=51°} \end{gathered}$$
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