Question

1. understand in the figure at the right, ∠lmn is bisected twice to form ∠lmk. how is the measure of ∠lmk related to the measure of ∠lmn?

Explanation:

Step1: Recall angle - bisection concept

When an angle is bisected, it is divided into two equal - sized angles. Let \(m\angle LMN=\theta\).

Step2: First bisection

When \(\angle LMN\) is bisected once, say by a ray \(MP\), then \(m\angle LMP = m\angle PMN=\frac{1}{2}m\angle LMN\).

Step3: Second bisection

If \(\angle LMP\) is bisected by ray \(MK\) to form \(\angle LMK\), then \(m\angle LMK=\frac{1}{2}m\angle LMP\).

Step4: Substitute

Since \(m\angle LMP=\frac{1}{2}m\angle LMN\), then \(m\angle LMK=\frac{1}{2}\times\frac{1}{2}m\angle LMN=\frac{1}{4}m\angle LMN\).

Answer:

The measure of \(\angle LMK\) is one - fourth of the measure of \(\angle LMN\).