Answer:

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Step-by-step explanation:

In △QOT&△ROS

∠QOT=∠ROS [vertically opposite angle ]

∠OQT=∠ORS [alternate interior angle ]

QT=RS [QT=PQ and PQ=RS]

△QOT≅△ROS (by AAS congruency rule)

⟹QO=RO (CPCT)

⟹O is the mid-point of QR

⟹ST bisects RQ.

Answer:

In the given figure, let's consider the parallelogram PQRS.

Since RS is produced to point T, we can see that angle RST is the exterior angle formed by the extension of side RS.

Given that angle RST is 110°, we know that the interior opposite angle, angle QSR, is supplementary to the exterior angle. So, angle QSR is 180° - 110° = 70°.

Since PQRS is a parallelogram, opposite angles are congruent. Therefore, angle PSR is also 70°.

Now, let's consider the interior angles at point S. Angle PSR is 70°, and since opposite angles are congruent, angle SRQ is also 70°.

Finally, we can find the remaining angle of the parallelogram. Since the sum of angles in a quadrilateral is 360°, we can subtract the sum of the three known angles from 360° to find angle PQR.

Angle PQR = 360° - (70° + 70° + 70°) = 360° - 210° = 150°.

In summary, the measure of all the angles of the parallelogram PQRS are:

- Angle QSR = 70°

- Angle PSR = 70°

- Angle SRQ = 70°

- Angle PQR = 150°