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Question
In rectangle PAIR, find ∠ARI, ∠RMI and ∠PMA.
Solution
Given, ∠RAI = 35°
∴ ∠PRA = 35° ...[PR || AI and AR is transversal]
⇒ ∠ARI = 90° – ∠PRA
= 90° – 35°
= 55°
∵ AM = IM,
∠MIA + ∠MAI = 35°
In ΔAMI,
∠RMI = ∠MAI + ∠MIA = 70° ...[Exterior angle]
Also, ∠RMI = ∠PMA
⇒ ∠PMA = 70° ...[Vertically opposite angles]
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