Final answer:
To construct an angle with specific measurements using a straightedge and compass, one must follow geometric instructions (C), since these tools don't measure angles directly but create the desired angle through a series of constructions. The correct answer is C) Follow geometric instructions
Step-by-step explanation:
The question asks how to construct an angle with specific measurements using a straightedge and compass. The correct answer is C) Follow geometric instructions. Unlike a protractor or a surveyor's telescope, which can measure angles directly, geometric construction using a straightedge and compass does not involve measurement but rather a series of steps to create the desired figure. To construct a specific angle, one would need to follow a set of geometric instructions that allow for the creation of the required angle through a combination of drawing circles and lines.
For example, to construct a 60-degree angle, one would start by drawing a base line with a straightedge. Then, using a compass, one would draw a circle centered at one end of the line. Where this circle intersects the base line marks the vertex of the angle. Without changing the compass width, you place the compass on this intersection point and make an arc that crosses the first circle. The point where the arcs intersect marks the second arm of the angle. Connecting this point to the vertex with a straightedge completes the 60-degree angle through a series of steps without measuring the angle directly.