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

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

Solution:

Given, PAIR is a rectangle.

We have to find the measures of ∠ARI, ∠RMI and ∠PMA.

We know that the diagonals of a rectangle are equal in length.

Since PR || AI, the corresponding angles are equal.

∠RAI = ∠PRA

Given, ∠RAI = 35°

So, ∠PRA = 35°

We know that each angle in a rectangle is equal to 90 degrees.

So, ∠ARI + ∠PRA = 90°

35° + ∠ARI = 90°

∠ARI = 90° - 35°

∠ARI = 55°

The diagonals PI and AR bisect at M.

So, AM = MR = PM = MI

∠MIA = ∠MAI

Given, ∠MAI = 35°

So, ∠MIA = 35°

Considering triangle AMI,

∠RMI = ∠MAI + ∠MIA

∠RMI = 35° + 35°

∠RMI = 70°

We know that the vertically opposite angles are equal.

So, ∠RMI = ∠PMA

Therefore, ∠PMA = 70°

✦ Try This: In Parallelogram PAIR, find ∠ARI, ∠RMI and ∠PMA.

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 5 Problem 145

Summary:

In rectangle PAIR, the measure of angles ∠ARI, ∠RMI and ∠PMA are 55°, 70° and 70°.

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