Question

im dum as heck but could anyone better explain how i do this question to me or help me in general do it Please my parents are rlly upset with me

Answer 1

Answer:

(10-2) x 180

= 1440 is the sum of interior angles

Step-by-step explanation:

use the equation (n-2) x 180

where n = the number of sides

Answer 2

How many triangles are there in the polygon, from one vertice?

Consider dividing the shape into pieces.

If the polygon is $\rm n$-sided, the diagonal we can draw from one vertice is exactly $\rm n-3$. We can't connect itself and the adjacent vertices.

The diagonal will divide the triangle into exactly $\rm n-2$ pieces. This is due to the first diagonal divides the shape into two pieces.

There exist exactly $\rm n-2$ triangles, and each of them has $180^{\circ}$ as the sum of angles!

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$\textbf{- Angle Sum}$

$\boxed{\rm (n-2)\times180^{\circ}}$

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Since we have a 10-sided regular polygon, the sum of its all angles is where $\rm n=10$.

$\rm (n-2)\times180^{\circ},\ n=10$

$\rm =8\times180^{\circ}$

$=1440^{\circ}$

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This is the main idea of the formula!

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$\Large\textrm{Learn More}$

$\textbf{- An Angle of the Regular Polygon}$

$\boxed{\rm \dfrac{(n-2)}{n}\times180^{\circ}}$

All angles are equal in a regular polygon, so if the regular polygon is $\rm n$-sided, there are $\rm n$ angles, so we divide it.