9514 1404 393
Answer:
- ∠PTQ = 45°
- ∠QTR = 15°
- ∠PTS = 120°
Step-by-step explanation:
Parallelogram PTSR is divided into two equilateral triangles by diagonal RT. All of the acute angles in that quadrilateral are 60°, and the obtuse angles are 120° (2×60° and also the supplement of 60°).
Triangle PTQ is an isosceles right triangle, so its acute angles are 45°.
∠PTQ = 45°
∠QTR = ∠PTR -∠PTQ = 60° -45°
∠QTR = 15°
∠PTS = 120° . . . . . . obtuse angle in PTSR; sum of ∠PTR and ∠RTS
