What is the sum of 3 of the interior angles of a regular hexagon?
The correct answer and explanation is:
The sum of three interior angles of a regular hexagon is 360°.
To understand this, it is important to know the properties of a hexagon and how interior angles work. A hexagon is a polygon with six sides. In any polygon, the sum of the interior angles can be calculated using the formula: Sum of Interior Angles=(n−2)×180∘\text{Sum of Interior Angles} = (n – 2) \times 180^\circ
where nn is the number of sides of the polygon. For a hexagon, n=6n = 6, so: Sum of Interior Angles=(6−2)×180∘=4×180∘=720∘\text{Sum of Interior Angles} = (6 – 2) \times 180^\circ = 4 \times 180^\circ = 720^\circ
This means the sum of all interior angles of a hexagon is 720°. Since the hexagon is regular, all its interior angles are equal. To find the measure of each interior angle, divide the total sum by the number of sides (6): Each Interior Angle=720∘6=120∘\text{Each Interior Angle} = \frac{720^\circ}{6} = 120^\circ
Now, if we want the sum of three interior angles, we simply multiply the measure of one angle by 3: Sum of Three Interior Angles=120∘×3=360∘\text{Sum of Three Interior Angles} = 120^\circ \times 3 = 360^\circ
Thus, the sum of three interior angles of a regular hexagon is 360°. This calculation holds true because in any regular polygon, all interior angles are congruent, and the sum of multiple angles can be easily calculated by multiplying the number of angles by the measure of each angle.