Find the value of angle f.

The triangle in option f) is isosceles because it has two sides with the same length as indicated by the ticks on the sides. In an isosceles triangle, the angles opposite the equal sides are also equal. Therefore, the angle opposite the other equal side is 75 degrees. The sum of the angles in any triangle is 180 degrees. We can write the equation: $$75^{\circ} + 75^{\circ} + f = 180^{\circ}$$ Now, let's solve for f: $$150^{\circ} + f = 180^{\circ}$$ $$f = 180^{\circ} - 150^{\circ}$$ $$f = 30^{\circ}$$ Answer: 30 degrees