Select the related word from the given alternatives so that the analogy Square : 90 degree :: Equilateral triangle : ? is correctly completed.

Introduction / Context:
This analogy problem tests basic knowledge of geometry, specifically the measures of interior angles in standard shapes. Understanding the angle properties of squares and equilateral triangles is fundamental in school level mathematics and is often assessed through analogy style questions in aptitude exams.

Given Data / Assumptions:
First pair: Square : 90 degree. Second pair: Equilateral triangle : ?. The degree values refer to interior angles of the shapes. Each option represents a possible measure of an interior angle.

Concept / Approach:
In a square, each interior angle measures 90 degrees. Therefore, the relationship in the first pair is shape to measure of each of its interior angles. To complete the analogy, we must determine the measure of each interior angle in an equilateral triangle. Remember that an equilateral triangle has all three sides equal and also all three angles equal, and the sum of interior angles of any triangle is 180 degrees.

Step-by-Step Solution:
Step 1: Recall the angle property of a square. A square has four right angles, each measuring 90 degrees. Step 2: Identify the relationship. The shape is linked to the measure of each interior angle. Step 3: Recall the angle sum of a triangle. The sum of all interior angles of any triangle is 180 degrees. Step 4: Use the property of an equilateral triangle. An equilateral triangle has three equal sides, so all three angles are equal too. Step 5: Compute each angle. Each angle = total sum of angles / number of angles = 180 / 3. 180 / 3 = 60. Therefore, each angle in an equilateral triangle measures 60 degrees.

Verification / Alternative check:
We can check consistency by comparing the structure of the statements. In the first pair, we can say every interior angle of a square measures 90 degrees. In the second, every interior angle of an equilateral triangle measures 60 degrees. Both statements parallel each other and clearly show the same type of relationship. This confirms that 60 degree is the only value that completes the analogy correctly.

Why Other Options Are Wrong:
30° is too small and would make the total of three angles only 90 degrees, which is not a valid triangle. 90° would imply a right angle triangle if only one angle is 90 degrees, or would sum to 270 degrees if all three were right angles, which is impossible. 120° would create an angle sum of 360 degrees for three equal angles, which is not valid for a triangle. 45° leads to a total of 135 degrees for three equal angles, which is again not equal to 180 degrees.

Common Pitfalls:
Some learners may confuse the angle properties of different regular polygons. For example, they might remember that regular hexagons and other polygons have different interior angle measures and mix these values. A reliable habit is to quickly verify the angle sum and divide it by the number of sides for regular polygons. This straightforward method removes guesswork and ensures correct analogical reasoning in questions of this type.

Final Answer:
The analogy Square : 90 degree :: Equilateral triangle : ? is correctly completed by 60°.