Find the interior angles of a regular nonagon and a regular 100-gon

Mathematics

1 answer:

Vanyuwa [196]4 years ago

4 0

Answer:

nonagon: 140°

100-gon: 176.4°

Step-by-step explanation:

A regular polygon is one that has all sides the same length and all internal angles the same measure. A "nonagon" has nine (9) sides. An image of one is attached. There are some interesting relationships among the angles shown.

The figure can be divided into 9 congruent triangles. Each has a vertex at the center of the figure, and the other two vertices are each end of one side. The central angle (40°) is the supplement of the interior angle at each vertex of the nonagon (140°). Obviously, the central angles sum to 360° (one full circle), so each one has a measure that is 360° divided by the number of sides:

360°/9 = 40°

So, we can figure the interior angle (at the vertex) by subtracting from 180° the value of 360° divided by the number of sides.

For the 100-gon, with 100 sides, the interior angle will be ...

180° -360°/100 = 180° -3.6° = 176.4°

You might be interested in

Miles had a piece of paper 1/4 of a large circle cut in three equal parts from the center point of the circle. What angle is the

telo118 [61]

The angle of 1/4 of a circle is given by:
(1/4) * (360) = 90 degrees
We now look for the angle that results from dividing 1/4 of a circle into three equal parts.
We have then:
(1/3) * (90) = 30 degrees.
Answer:
the measure of each part is:
30 degrees

6 0

3 years ago

What is the area of a rectangle with side lenghts 3x+2 and x-4

melamori03 [73]

For a rectangle, A = LW.

A = (3x + 2)(x - 4)

A = 3x^2 - 12x + 2x - 8

A = 3x^2 -10x - 8

6 0

4 years ago

Help:<br> <img src="https://tex.z-dn.net/?f=1.%5C%20%26x%5E4-61x%5E2%2B900%3D0%20%5C%5C%202.%20%5C%20%26%20x%5E4-25x%5E2%2B144%3

yawa3891 [41]

$\bf{1) \ x^4-61x^2+900=0 }$