Question
In rectangle $PAIR$, find $\angle\text{ARI},\angle\text{RMI}\ \text{and}\angle\text{PMA}.$
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Answer
Given, $\angle\text{RAI}=35^\circ$
$\angle\text{PRA}=35^\circ$
$\angle\text{ARI}=90^\circ-\angle\text{PRA}=90^\circ-35^\circ=35^\circ$
$\text{AM}=\text{IM},\angle\text{MIA}=\angle\text{MAI}=35^\circ$
$\text{In}\triangle\text{AMI},\angle\text{RMI}=\angle\text{MAI}+\angle\text{MIA}=70^\circ$ [exterior angle] Also, $ \angle\text{RMI}=\angle\text{PMA}$
$ \angle\text{PMA}=70^\circ$ [Vertically opposite angles]
$\angle\text{PRA}=35^\circ$
$\angle\text{ARI}=90^\circ-\angle\text{PRA}=90^\circ-35^\circ=35^\circ$
$\text{AM}=\text{IM},\angle\text{MIA}=\angle\text{MAI}=35^\circ$
$\text{In}\triangle\text{AMI},\angle\text{RMI}=\angle\text{MAI}+\angle\text{MIA}=70^\circ$ [exterior angle] Also, $ \angle\text{RMI}=\angle\text{PMA}$
$ \angle\text{PMA}=70^\circ$ [Vertically opposite angles]
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