What are the interior and exterior angles of a pentagon?
The General Rule
| Shape | Sides | Sum of Interior Angles |
|---|---|---|
| Triangle | 3 | 180° |
| Quadrilateral | 4 | 360° |
| Pentagon | 5 | 540° |
| Hexagon | 6 | 720° |
What are the exterior angles of a pentagon?
Answer: The measure of each exterior angle of a regular pentagon is 72° A regular pentagon has all angles of the same measure and all sides of the same length.
What are the interior and exterior angles of a decagon?
The sides and angles are congruent in a regular decagon. The characteristics of a regular decagon are: All sides are equal in length and all the angles are equal in the measure in a regular decagon. Each interior angle in regular decagon measures 144º, while each exterior angle measures 36º.
What is one exterior angle of a decagon?
36°
Since each exterior angle and interior angle form a linear pair, one exterior angle of a decagon = 180 – 144 = 36°. We know that a decagon had 10 exterior angles, so, 10 × 36 = 360°. Hence, it is seen that the sum of the exterior angles of a decagon is 360°.
What is the sum of interior angles of a decagon?
1440°
Decagon/Sum of interior angles
How do you find the interior angles of a pentagon?
Method 1
- The exterior angle is 360 ÷ 5 = 72 ∘ .
- The interior angle is 180 − 72 = 108 ∘ .
- The sum of interior angles is ( 5 − 2 ) × 180 = 540 ∘ .
- The interior angle is 540 ÷ 5 = 108 ∘ .
- The exterior angle is 180 − 108 = 72 ∘ .
How do you find the interior angle of a pentagon?
What is the sum of all exterior angles of a pentagon?
360°
This means: Sum of exterior angles = 180n – 180(n-2) = 180n – 180n + 360. Hence, the sum of exterior angles of a pentagon equals 360°.
What is the sum of the interior angles of a pentagon?
540°
Pentagon/Sum of interior angles
What is each angle of a pentagon?
108 degrees
Each interior angle of a pentagon is 108 degrees.
What is the sum of exterior angles of a pentagon?
What are the exterior angles of a decagon?
Decagon Angles. In many decagons, the sum of interior angles will be 1,440° 1,440 °, but that is not an identifying property because complex decagons will not have that sum. Regular decagons have two additional identifying properties: 10 exterior angles of 36° 36 °, summing to 360° 360 °.
How many sides does a complex decagon have?
In crossing its own sides, a complex decagon sets off additional interior spaces, but it is still said to have only 10 sides, 10 interior angles, and 10 vertices. Because it is so highly irregular and self-intersecting, a complex decagon need not follow any predictable rule about interior angles or their sums.
Which is an identifying property of a decagon?
In many decagons, the sum of interior angles will be 1,440° 1,440 °, but that is not an identifying property because complex decagons will not have that sum. Regular decagons have two additional identifying properties:
Why are decagons called many-angled polygons?
Decagons belong to the family of two-dimensional shapes called polygons. Polygons get their name from Greek, meaning “many-angled,” because all polygons have multiple interior angles. They close in a two-dimensional space using only straight sides.