In each of the following questions, choose the word that is most similar in meaning to the word given in capitals. Here, the word is ESTRANGE, which is often used for relationships that have become distant.

Introduction / Context:
This question tests your understanding of the vocabulary word ESTRANGE. Such words are frequently used to describe changes in relationships, particularly when people who were once close gradually become distant. Knowing the correct synonym is useful both for reading comprehension and for precise expression in English. You must select the option that best matches the idea of estranging someone.

Given Data / Assumptions:
- Target word: ESTRANGE. - Options: Endanger, To become puzzling, Miscalculate, Alienate. - Only one option correctly captures the meaning of estranging someone.

Concept / Approach:
Estrange means to cause someone to no longer be close or friendly with another person or group. It describes the process of turning a friend into a stranger or creating emotional distance. The closest common synonym in everyday English is alienate. Alienate means to cause someone to feel isolated, unfriendly, or no longer supportive. The other options relate to risk, confusion, or calculation and do not match this emotional or relational context. By focusing on the relational meaning, you can quickly identify the correct option.

Step-by-Step Solution:
Step 1: Recall that estranging someone usually means causing a loss of affection, closeness, or friendly feeling. Step 2: Look at option A, Endanger, which means to put at risk or in danger. This deals with safety, not relationships. Step 3: Look at option B, To become puzzling, which suggests becoming confusing. Estrange does not mean to confuse. Step 4: Look at option C, Miscalculate, which deals with making an error in judgment or arithmetic and has no link to relationships. Step 5: Look at option D, Alienate, which means to cause someone to feel isolated or no longer friendly. This closely matches the meaning of estrange.

Verification / Alternative check:
Consider example sentences to verify. One might say constant quarrels estranged him from his family, meaning constant quarrels alienated him from his family. Replacing estranged with alienated keeps the sense of separation and distance. However, using endanger, become puzzling, or miscalculate would produce sentences that do not make logical sense. This shows that alienate is the only choice that fits both logically and semantically, confirming it as the correct synonym.

Why Other Options Are Wrong:
Endanger is wrong because it refers to putting someone at risk, usually of harm or loss, not emotional distance. To become puzzling is wrong because estranging someone does not mean making a situation confusing. Miscalculate is wrong as it refers to incorrect calculation or judgment, not to relationships.

Common Pitfalls:
Some learners confuse estranged with strange and think it simply means odd. In fact, estranged is about relationships that have become distant. Others may overfocus on the sound of the word and guess randomly among options. To avoid mistakes, associate estranged with alienated and remember collocations like estranged husband, estranged relatives, and estranged friend. Consistently noticing such phrases while reading newspapers or novels strengthens your memory of the word and its correct synonym.

Final Answer:
The word most similar in meaning to ESTRANGE is Alienate.