Question

which construction correctly shows how to bisect ∠x? a diagram of angle with a line, b diagram of angle with arcs, c diagram of angle with more arcs, d diagram of angle with an arc

Explanation:

Step1: Recall the steps of angle - bisector construction

To bisect an angle \(\angle X\), first, with the vertex \(X\) as the center, draw an arc that intersects both sides of the angle. Then, with the intersection points of the arc and the sides of the angle as centers (using the same radius), draw two more arcs that intersect each other. The ray from \(X\) through this intersection point is the angle - bisector.

Step2: Analyze each option

• Option A: There are no arcs drawn, so it does not show the construction steps of an angle - bisector.
• Option B: Only one arc (the first arc of the angle - bisector construction) is drawn, but the second - stage arcs (to find the intersection point for the bisector ray) are missing.
• Option C: First, an arc is drawn with vertex \(X\) as the center intersecting the two sides of \(\angle X\). Then, with the intersection points of the first arc and the sides of the angle as centers, two arcs are drawn which intersect each other. This follows the correct construction steps of an angle - bisector.
• Option D: The first arc (with vertex \(X\) as the center) is missing.

Answer:

C.