In basic geometry, how many right angles does a square have?

Difficulty: Easy

Correct Answer: 4

Explanation:


Introduction / Context:
Squares are among the most familiar shapes in plane geometry. They are special quadrilaterals that are both rectangles and rhombuses. Understanding the angle properties of a square is essential for many basic geometry questions, including those involving area, perimeter and symmetry.


Given Data / Assumptions:
- A square is a quadrilateral with four equal sides.
- All interior angles of a square are right angles.
- A right angle measures exactly 90 degrees.
- We are asked how many right angles are present in a square.


Concept / Approach:
By definition, a square is a special rectangle. A rectangle is a quadrilateral with four right angles. Since a square satisfies the definition of a rectangle, it also has four right angles. The additional property of a square is that all its sides are equal in length. Therefore, we simply need to recall the angle property of rectangles and squares.


Step-by-Step Solution:
Step 1: Recall that any quadrilateral has four interior angles. Step 2: By definition, a square is a quadrilateral where each interior angle is a right angle of 90 degrees. Step 3: Since there are four corners (vertices) in a square, and each corner contains a right angle, the total number of right angles is 4. Step 4: No additional interior angles exist beyond these four, so the answer is fixed and straightforward.


Verification / Alternative Check:
You can verify this by drawing a square on graph paper. Each corner clearly forms an L shape, which measures 90 degrees. Measuring with a protractor would confirm that each interior angle is a right angle. There is no possibility of more or fewer right angles in a standard square.


Why Other Options Are Wrong:
Option A (2) is wrong because it suggests that only two angles are right, which would not satisfy the definition of a square or a rectangle.
Option B (6) and Option D (8) are not possible counts for interior angles of any quadrilateral, since a quadrilateral has only four vertices and thus four interior angles.


Common Pitfalls:
Sometimes learners confuse the total count of right angles with the total measure of all angles in the shape. While the sum of interior angles in any quadrilateral is 360 degrees, what matters here is the number of 90 degree angles, not their sum. All four angles in a square are right angles.


Final Answer:
A square has 4 right angles.

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