For a decagon (ten - sided polygon), find a. The number of diagonals drawn from one vertex. b. The number of triangles formed by the diagonal from one vertex. c. The sum of interior angles of the decagon. For the given figure,

Question

UpStudy AI · Accepted Answer

**a. Number of diagonals from one vertex**

A vertex in an $$ n $$-sided polygon can be connected to all other vertices except itself and its two adjacent vertices. For a decagon ($$ n=10 $$):

$$
\text{Number of diagonals} = n - 3 = 10 - 3 = 7
$$

**b. Number of triangles formed by the diagonal from one vertex**

When all diagonals are drawn from one vertex in a polygon, they divide the polygon into triangles. The number of triangles formed is always:

$$
\text{Number of triangles} = n - 2 = 10 - 2 = 8
$$

**c. Sum of interior angles of the decagon**

The formula for the sum of the interior angles of an $$ n $$-sided polygon is:

$$
\text{Sum of interior angles} = (n - 2) \times 180^\circ
$$

For a decagon:

$$
\text{Sum} = (10 - 2) \times 180^\circ = 8 \times 180^\circ = 1440^\circ
$$
**a. Number of diagonals from one vertex:** 7 **b. Number of triangles formed by the diagonal from one vertex:** 8 **c. Sum of interior angles of the decagon:** 1440 degrees

For a decagon (ten - sided polygon), find a. The number of diagonals drawn from one vertex. b. The number of triangles formed by the diagonal from one vertex. c. The sum of interior angles of the decagon. For the given figure,

Upstudy AI Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Geometry Questions