Question

please solve it
In rectangle PAIR. <RAI=35" Find <ARI and <PMA​ .

answers are 55 , 70 and 70 please solve and send
who will give the right answer I will give your brain list To him or her ​​

Answer 1

Answer:

Follow me and mark me as brainlist and give me 10 thanks

Answer 2

To Find:-

∠ARI and ∠PMA

SOLUTION:-

□ PAIR is a rectangle.

•°• All interior angles are 90° .....{a}

•°• RI = PA and PR = AI .....{b}

In △RIA, ∠RAI = 35°

∠RIA = 90° ....{from a}

•°• sum all angles of triangle is 180°

∠RAI + ∠RIA + ∠ARI = 180°

35 + 90 + ∠ARI = 180

∠ARI = 180 - 125

∠ARI = 55°

now, we will find ∠PMA

RI = PA .....from {b}

and RI || PA .....{sides of rectangle}

∠PAR = ∠ARI .......{Alternate angle}

That means,

∠PAM = ∠ARI

•°• ∠PAM = 55°

now,

Diagonal PI and RA bisect each other at M.

•°• PI = RA

•°• PM = MI = AM = MR .......{c}

•°• PM = MA ....{fromc}

Therefore △PMA is is Isosceles

as PM = MA

•°• ∠PAM = ∠APM ....{angles opposite to congruent sides are congruent}

•°• ∠APM = 55°

In △PMA, ∠PAM = ∠APM = 55°

Sum of all angle = 180°

∠PAM + ∠APM + ∠PMA = 180°

55 + 55 + ∠PMA = 180

∠PMA = 180 - 110

∠PMA = 70°

Answer is => ∠ARI = 55° and ∠PMA = 70° .

Note: {Each diagonal bisects the other. In other words, the point where the diagonals intersect (cross), divides each diagonal into two equal parts}