Mathematics, 30.12.2019 12:31 nnagg0ll

Find the measure of each interior angle and each exterior angle of the following regular polygons. show your work

Find the measure of each interior angle and each exterior angle of the following regular polygons. s

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Answer from: joseperez1224

$\bf \textit{sum of all interior angles of a regular polygon}\\\\
n\theta =180(n-2)\qquad 
\begin{cases}
n=\textit{number of sides}\\
\theta =\textit{interior angle}
\end{cases}\\\\
-------------------------------\\\\
\textit{sum of all exterior angles of a regular polygon}\\\\
n\theta =360\qquad 
\begin{cases}
n=\textit{number of sides}\\
\theta =\textit{interior angle}
\end{cases}$

now, with that in mind... let's take a peek at .. hmmm say c) dodecagon
now, a Dodecagon has 12 sides.... let's check the angles then

$\bf n\theta =180(n-2)\qquad n=12\implies 12\theta =180(12-2)
\\\\\\
12\theta =180\cdot 10\implies 12\theta =180\implies \theta =\cfrac{1800}{12}
\\\\\\
\theta =150^o\impliedby \textit{interior angle of a Dodecagon}\\\\
-------------------------------\\\\
n\theta =360\qquad n=12\implies 12\theta =360\implies \theta =\cfrac{360}{12}
\\\\\\
\theta =30^o\impliedby \textit{exterior angle of a Dodecagon}$

so... hmm now for a) a decagon is 10 sides, b) pentagon is 5 sides, d) and e) pretty much you can tell how many sides on those already.

Answer from: stace49

Step-by-step explanation:

As we know for a regular polygon sum of all interior angles is represented by n A = 180 (n-2)

and sum of all exterior angles is represented by n A' = 360°

Here n represents number of sides of the polygon.

Now we will go for each options given.

(A) Decagon : (Having 10 sides)

(1) 8A = 180 ( 8-2 )

8A = 180 × 6

A = $\frac{1080}{8}$ = 160° ( interior angle )

(2) n A' = 360°

8 A' = 360°

A = 45° ( exterior angle )

(B) Pentagon ( having 5 sides )

(1) 5A = 180 ( 5-2 )

5A = 180 × 3 = 540

A = 108° ( interior angle )

(2) 5A' = 360

A' = 72° (exterior angle )

(1) 12A = 180 (12-2)

12 A = 180 × 10 = 1800

A = 150° ( interior angle )

(2) 12 A' = 360

A' = 30° ( exterior angle )

(D) 16-gon ( having 16 sides )

(1) 16 A = 180 ( 16 - 2 )

16A = 180 × 14

16 A = 1520

A = 157.5° ( interior angle )

(2) 16 A' = 360

A' = 22.5°

(E) 25-gon ( having 25 sides )

(1) 25 A = 180 ( 25-2)

25A = 180 (23)

A = 165.6° ( interior angle )

(2) 25A' = 360

A = 14.4° ( exterior angle)

Answer from: Quest

step-by-step explanation:

Answer from: Quest

answer: 140

step-by-step explanation:

so just add all then it will be your answer but i am not pretty sur eif it is but hope this i am here to people

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