Question

question 2 of 25

to trisect a(n) ______ angle, you first construct an equilateral triangle.

a. 60-degree
b. acute
c. obtuse
d. right

Explanation:

Analyze the construction goal

Using the Angle Trisection and Compass and Straightedge Construction knowledge points:
To trisect a given angle means to divide it into three equal angles using only a compass and straightedge. While trisecting an arbitrary angle is impossible, certain specific angles can be trisected.

Evaluate the construction steps

Using the Compass and Straightedge Construction knowledge point:

1. Constructing an equilateral triangle creates angles of \(60^\circ\).
2. Trisecting a \(90^\circ\) (right) angle yields three \(30^\circ\) angles.
3. A \(30^\circ\) angle is easily constructed by bisecting a \(60^\circ\) angle of an equilateral triangle.
4. Therefore, to trisect a right angle, one first constructs an equilateral triangle to obtain a \(60^\circ\) angle, which is then subtracted from the \(90^\circ\) angle to leave \(30^\circ\), or bisected to construct the required \(30^\circ\) divisions.

Answer:

• (A) 60-degree
• (B) acute
• (C) obtuse
• (D) right (Correct answer)