Question

In the figure shown below, PQRS is a square and TPS is an equilateral triangle. The bisectors of angle PTS and angle QRS meet at point O. What is the measure of angle TOR?​

Answer 1

Answer:

120*

Step-by-step explanation:

aka p show for cold PA

Answer 2

Drawing: refer to the attachment

We name the intersection of PS and TO, U.

Step-by-step explanation:

Since TO is the bisector of ∠PTS, ΔPTS being an equilateral triangle, TO ⏊ PS.

Thus ∠SUO = 90°

Since PQRS is a square, ∠RSU = 90°

Given that, OR is the angle bisector of ∠QRS.

Then ∠ORS = 45°, since PQRS is a square and ∠QRS = 90°

From the quadrilateral SUOR, we write

∠UOR + ∠ORS + ∠RSO + ∠SUO = 360°

or, ∠TOR + 45° + 90° + 90° = 360°, since ∠UOR = ∠TOR

or, ∠TOR + 225° = 360°

or, ∠TOR = 135°

Answer:

The measure of ∠TOR is 135°.

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