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A robot is initially facing a direction defined as $0^{\circ}$. It rotates $60^{\circ}$ to its left. Then, it rotates another $30^{\circ}$ to its left. What is its final orientation in degrees, relative to its starting direction (assuming left turns correspond to positive angle changes)?
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A point starts at coordinates $(2, 3)$ on a Cartesian plane. It moves 4 units horizontally in the positive x-direction, and then 5 units vertically in the positive y-direction. What are its new coordinates?
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A surveyor needs to mark the boundary of a square plot of land. Each side of the square is 25 meters long. If the surveyor starts at one corner and walks along all four sides to return to the starting point, what is the total distance walked?
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To form a regular pentagon, one must make equal turns at each vertex after drawing each side. The interior angle of a regular pentagon is $108^{\circ}$. What is the measure of the exterior angle (the turn angle) one must make at each vertex?
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An object starts at the origin $(0,0)$ of a coordinate plane. It moves according to the following sequence of displacements:
- Step 1: Moves from $(0,0)$ to $(4,0)$.
- Step 2: Moves from $(4,0)$ to $(4,3)$.
- Step 3: Moves from $(4,3)$ to $(0,3)$.
- Step 4: Moves from $(0,3)$ back to $(0,0)$.
What is the geometric shape traced by this path? Calculate the total length of the path (the perimeter of the shape).