Answer: The Answer for your question is 62 because
Step-by-step explanation:
In a rectangle, the diagonals are equal in length and bisect each other, which means they intersect at a 90° angle. Therefore, the triangle PTS is a right triangle with ∠PTS = 34°. This implies that ∠TPS = 90° - 34° = 56°.
Since ∠TPS and ∠TQR are corresponding angles of parallel lines TP and QR (since QRST is a rectangle), they are equal. Therefore, ∠TQR = 56°.
Now, in triangle QTR, we know that ∠TQR = 56° and ∠QTR + ∠RTQ = 180° - ∠TQR = 124°. Since QTR is an isosceles triangle (as TQ = TR, because diagonals of a rectangle are equal), ∠QTR = ∠RTQ. Therefore, each of these angles is 124°/2 = 62°.
So, m∠QTR = 62°.
