Question

Inscribe an equilateral triangle inside the circle using only a compass and a straightedge. What is the sum of the interior angles of this equilateral triangle?

a) 90 degrees
b) 120 degrees
c) 180 degrees
d) 360 degrees

Answer 1

To inscribe an equilateral triangle inside a circle using a compass and straightedge, draw a diameter, place arcs on the diameter, connect the intersections, and complete the triangle. The sum of the interior angles of an equilateral triangle is always 180 degrees.

Step-by-step explanation:

To inscribe an equilateral triangle inside a circle using only a compass and a straightedge, follow these steps:

1. Draw a line segment that represents the diameter of the circle.
2. Place the compass at one end of the diameter and draw an arc intersecting the diameter.
3. Without changing the compass width, place the compass at the other end of the diameter and draw another arc intersecting the diameter.
4. Connect the two points where the arcs intersect the diameter. This forms the base of the equilateral triangle.
5. Use the compass to draw arcs from the two endpoints of the base, intersecting at a point above the base.
6. Connect the two endpoints of the base with the point of intersection of the arcs. This forms the equilateral triangle inscribed inside the circle.

The sum of the interior angles of an equilateral triangle is always 180 degrees. Therefore, the correct answer is c) 180 degrees.