‘What is the sum of 6 of the interior angles of a regular decagon?’
The correct answer and explanation is:
The sum of 6 interior angles of a regular decagon is 720 degrees.
Here’s the explanation:
A decagon is a polygon with 10 sides. To find the measure of each interior angle in a regular decagon (where all sides and angles are equal), first find the sum of all the interior angles of the decagon.
The formula for the sum of the interior angles of any polygon with nn sides is: Sum of interior angles=(n−2)×180∘\text{Sum of interior angles} = (n – 2) \times 180^\circ
For a decagon, n=10n = 10, so: (10−2)×180∘=8×180∘=1440∘(10 – 2) \times 180^\circ = 8 \times 180^\circ = 1440^\circ
This means the total sum of all interior angles in a decagon is 1440 degrees.
Since it is a regular decagon, each interior angle is equal. To find the measure of one interior angle: One interior angle=1440∘10=144∘\text{One interior angle} = \frac{1440^\circ}{10} = 144^\circ
The question asks for the sum of 6 of these interior angles. Multiply the measure of one interior angle by 6: 6×144∘=864∘6 \times 144^\circ = 864^\circ
Therefore, the sum of 6 interior angles of a regular decagon is 864 degrees.
If the question intended the sum of 6 any interior angles (not necessarily consecutive), since the polygon is regular, any 6 interior angles will sum to the same result.
To summarize:
- Total interior angle sum of decagon = 1440 degrees
- Each interior angle = 144 degrees
- Sum of 6 interior angles = 6 × 144 = 864 degrees