If each interior angle of a regular polygon measures 120 , how many sides does the polygon have?
2 answers:
- Each interior angle of regular polygon is 120°
- Number of sides of the polygon
Interior angle of the polygon = [180(n - 2)]/n
where,
- n = sides of the polygon
Let, The number of sides of polygon be n
<h3>By substituting values according to the formula,</h3>➯ [180(n - 2)]/n = 120°
➯ 180n - 360 = 120n
➯ 180n - 120n = 360
➯ 60n = 360
➯ n = 360/60
➠ n = 6
<h3><u>Hence, The regular polygon have 6 sides</u></h3>You might be interested in
Answer:
x ≈ 48.2°
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos x = =
, then
x = (
) ≈ 48.2° ( to the nearest tenth )
Answer:
Part A)
The <em>x-</em>intercepts are (-1/4, 0) and (4, 0).
Part B)
The vertex is a maximum because the leading coefficient is negative.
The vertex is (1.875, 72.25).
Part C)
We can plot the zeros and the vertex, and connect them with a curve.
Step-by-step explanation:
The function given is:
Part A)
To find the <em>x-</em>intercepts of the function, set the function equal to 0 and solve for <em>x: </em>
<em /><em />
We can divide both sides by negative four:
Factor:
Zero Product Property:
Solve for each case:
Hence, our zeros are:
Part B)
Note that the leading coefficient of our function is negative.
So, our function will be concave down.
Hence, our vertex will be the maximum.
The vertex is given by:
In this case, <em>a </em>= -16, <em>b</em> = 60, and <em>c</em> = 16.
Find the <em>x-</em>coordinate of the vertex:
Substitute this back into the function to find the <em>y-</em>coordinate:
Hence, our vertex is:
Part C)
Since we already determined the zeros and the vertex, we can plot the two zeros and the vertex and draw a curve between the three points.
The graph is shown below. Again, to do this by hand, simply plot the three points and connect them with a parabola. If necessary, we can also find the <em>y-</em>intercept.
