Geometry

Question Analysis

This question pertains to leveraging angle congruence to determine an unknown angle measure. The main emphasis lies in correctly applying the principle of congruent angles.

 

Key Concept Explanation

When two angles are congruent, denoted as ∠A ≌ ∠B, it implies that their measures are equal, i.e., m∠A = m∠B.

 

Step - by - Step Solution

1. We are given that ∠RST ≌ ∠LMN.

2. Given m∠NML = 144°. Since ∠NML is the same angle as ∠LMN (just with the vertex letter in a different position), and because of the congruence between ∠RST and ∠LMN, we can conclude that m∠TSR = m∠RST = m∠LMN = m∠NML = 144°.

 

Option Analysis

A.112°: This is the measure of ∠HGF, which is not relevant to the congruence pair for ∠TSR.

B.144°: Correct, as it is derived from the congruence relationship between ∠RST and ∠LMN.

C.32°: There is no basis for this value in the given problem data.