Question

In rectangle PAIR, find ∠ARI, ∠RMI and ∠PMA.

Answer 1

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°