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

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Question

In rectangle PAIR, find

∠ A R I, ∠ R M I

and

∠ P M A

.

In Rectangle PAIR, Find ∠ARI,∠RMI And ∠PMA.

Answer:
:
Given,

∠ R A I = 35^{\circ}

.

∴ ∠ P R A = 35^{\circ}

. [

P R ∥ A I

and AR is transversal]

\Rightarrow ∠ A R I = 90^{\circ} - ∠ P R A = 90^{\circ} - 35^{\circ} = 55^{\circ}

.

∵ R M = I M, ∠ M R I = ∠ M I R = 55^{\circ}

.
In

Δ R M I,

∠ R M I + ∠ M R I + ∠ M I R = 180^{\circ}

. [Angle sum property]

\Rightarrow ∠ R M I = 180^{\circ} - 55^{\circ} - 55^{\circ} = 180^{\circ} - 110^{\circ} = 70^{\circ}

Also,

∠ P M A = ∠ R M I

[vertically opposite angles]

\Rightarrow ∠ P M A = 70^{\circ}

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