Question

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Explanation:

Analyze the transformation

The problem states that a translation maps \(\angle J\) onto \(\angle K\). A translation is a rigid motion, which is a type of Geometric Transformations.

Apply translation properties

Translations preserve angle measures. Therefore, if a translation maps \(\angle J\) onto \(\angle K\), the two angles must be congruent:

$$ \angle J \cong \angle K $$

This means their measures are equal:

$$ m\angle J = m\angle K $$

Evaluate the options

Let's look at the visible options:

• Option 1: \(\angle J\) is twice the measure of \(\angle K\). (False, they must be equal)
• Option 2: \(\angle H\) is twice the measure of \(\angle J\). (No basis for this)
• Since translations preserve angle measure, the correct statement must express that the measure of \(\angle J\) is equal to the measure of \(\angle K\).

Answer:

• (A) \(\angle J\) is equal to the measure of \(\angle K\) (Correct answer)
• (B) \(\angle J\) is twice the measure of \(\angle K\)
• (C) \(\angle H\) is twice the measure of \(\angle J\)