Question
What is the measure of each angle of a regular quadrilateral? If necessary, round to the nearest tenth.
Ask by Sandoval Bob. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Each angle of a regular quadrilateral measures \( 90.0^\circ \).
Solution
1. For any polygon with \( n \) sides, the sum of the interior angles is given by:
\[
S = (n-2) \times 180^\circ
\]
2. For a quadrilateral, \( n = 4 \). Substituting in the formula:
\[
S = (4-2) \times 180^\circ = 2 \times 180^\circ = 360^\circ
\]
3. Since the quadrilateral is regular, all four angles are equal. Thus, the measure of each angle is:
\[
\text{Angle} = \frac{360^\circ}{4} = 90^\circ
\]
Rounded to the nearest tenth, each angle measures \( 90.0^\circ \).
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Simplify this solution Mind Expander
In a regular quadrilateral, which is essentially a square, each angle measures 90 degrees. This is because the total sum of angles in any quadrilateral is 360 degrees, and when you divide that evenly among the four angles, you get 360° ÷ 4 = 90°. Interestingly, a square is not just about equal angles. It also has all sides of equal length! This symmetry makes it a favorite in architecture and design, symbolizing stability and balance. So, next time you see a square, remember, it's not just a pretty shape; it’s a geometrical superstar!
