В трапеции PZFT PZ = FT, ∠ZTP = 14° и ∠ZTF = 11°. Найдите угол PZT. Ответ дайте в градусах.

Since PZ = FT, the trapezoid is isosceles. Therefore, opposite angles are equal, and base angles are equal.
∠PZT = ∠FTZ and ∠ZPF = ∠TFP.
We are given ∠ZTP = 14° and ∠ZTF = 11°. This implies that ∠PTF = ∠ZTP + ∠ZTF = 14° + 11° = 25°.
In an isosceles trapezoid, the sum of adjacent angles between parallel sides is 180°. So, ∠PZT + ∠ZTF = 180° and ∠ZPF + ∠PTF = 180°.
However, the given angles ∠ZTP and ∠ZTF are adjacent angles at vertex T. The sum of angles at vertex T is ∠PTF. The problem statement seems to imply that ∠ZTP and ∠ZTF are parts of ∠PTF. If ∠PTF = 14° and ∠ZTF = 11°, then ∠PZT = 180° - 14° = 166°.
If ∠ZTP = 14° and ∠ZTF = 11°, and these are angles within the trapezoid, and PZ=FT, then it's an isosceles trapezoid. The angles at the base are equal. ∠PZT = ∠FTZ. ∠ZPF = ∠PTF. Also, consecutive angles between parallel sides sum to 180°. So ∠PZT + ∠ZTF = 180° and ∠ZPF + ∠PTF = 180°. If ∠ZTF = 11°, then ∠PZT = 180° - 11° = 169°. If ∠ZTP = 14°, then ∠PTF = 180° - 14° = 166°. This is contradictory. Let's assume ∠PZT and ∠FTZ are the non-parallel sides, and PZ and FT are the non-parallel sides. Then PZ=FT means it's an isosceles trapezoid. The angles at the base are equal. So ∠PZT = ∠FTZ and ∠ZPF = ∠PTF. Also, ∠PZT + ∠PTF = 180° and ∠ZPF + ∠FTZ = 180°. If ∠ZTP = 14° and ∠ZTF = 11°, and these are angles of the trapezoid, then ∠PTF = 14° and ∠PZT = 11° (if PZ || FT). But PZ=FT implies it's an isosceles trapezoid. Let's assume PZ and FT are the non-parallel sides. Then PZ=FT. The angles at the base are equal. Let's assume PT || ZF. Then ∠PZT + ∠ZTF = 180° and ∠ZPF + ∠PFT = 180°. If ∠ZTP = 14° and ∠ZTF = 11°, then ∠PTF = 14° + 11° = 25°. Then ∠PZT = 180° - 25° = 155°.