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If you are good in maths then solve this

If PQRS is a rectangle in which angle QPR=34°,find the measure of angle SQR.

Answer 1

hey mate !!

here is your answer:

angle QPR=34° (given)
so, angle SPR=90°-34° ( because all the angles of a rectangle are of 90°)
=56°
now, we have to find angle SQR

so, let us take triangle SPR and triangle RSQ

here, PS=QR ( because opposite sides of a rectangle are equal)
SR =SR ( common line)
PR=QS (diagonals of a rectangle are equal)

thus by SSS congurency triangle SPR is congurent to triangle RSQ

and by cpct angle SPR= angle SQR

that is angle SQR=56°

hope it helps!!

Answer 2

In a rectangle, sum of angle formed on the vertices of angle is 90°

So according to the statement above
Angle SPO + 34° = 90°

Angle SPO = 90° - 34°

=> angle SPO = 56°

We know that diagonals in a rectangle, are equal and bisect each other. Therefore
PO = SO

Now using isoceles triangle property we can conclude that angle PSO = angle SPO
(opposite angles to equal sides of a triangle hence equal)

This means angle PSO = 56°

We know that in a rectangle opposite sides are parallel and equal

this means, PQ ll SR and SQ is transversal.

So be alternate angle property we can say

angle PSO = angle SQR = 56°

Hence, angle SQR = 56°

Refer the attachment for figure (^^)"

Hope it helps dear friend ☺️✌️✌️