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Question
In rectangle PAIR, find ∠ARI, ∠RMI and ∠PMA.
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Solution
In ΔARI,
∠RAI + ∠AIR + ∠IRA = 180° ...[Angle sum property]
`\implies` 35° + 90° + ∠IRA = 180°
`\implies` ∠IRA = 180° – 125° = 55°
∴ ∠ARI = 55° ...(i)
Now, in ΔRMI,
Since, the diagonals of a rectangle are equal and they bisect each other
∴ MI = MR
`\implies` ∠MRI = ∠MIR = 55° ...[From (i)]
And ∠RMI + ∠MIR + ∠IRM = 180° ...[By angle sum property]
`\implies` ∠RMI + 55° + 55° = 180°
`\implies` ∠RMI = 180° – 110° = 70°
Now, ∠RMI = ∠PMA = 70° ...[∵ Vertically opposite angles]
Hence, ∠ARI = 55°, ∠RMI = 70° and ∠PMA = 70°
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