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the measure of the seven angles in a nonagon measure 138, 154, 145, 132, 128, 147 and 130. if the two remaining angles are equal in measure, what is the measure of each angle

Respuesta :

A polygon is any figure sided with three sides and above such that triangle (3) is the smallest polygon. A nonagon is a polygon with 9 sides. To get the sum of interior angles of a polygon we use the formula;
(n-2) 180 or (n-4)90 where n is the number of sides.
Therefore, for a nonagon the sum of interior angles = (9-2) 180 = 1260 degrees
If we add all the angles we should get 1260, considering the remaining angles to be each x
Thus 138+154 +145 +132 +128 +147 +130 + x +x =1260
                             = 974 + 2x = 1260
                             = 2x = 286
                             = 143
 therefore, each of the other angles was 143 
Lanuel

Since the two remaining angles are equal in measure, the measure of each angle is 143°.

  • Let the unknown angles be a.

Given the following data:

  • First angle = 138°
  • Second angle = 154°
  • Third angle = 145°
  • Fourth angle = 132°
  • Fifth angle = 128°
  • Sixth angle = 147°
  • Seventh angle = 130°

To find the two remaining angles:

A nonagon is a type of polygon that comprises nine (9) sides.

First of all, we would determine the sum of the interior angles of a nonagon by using the following formula:

[tex](n-2) \times180[/tex]

Where:

  • n is the number of sides of a polygon.

For a nonagon:

n = 9

[tex]Nonagon = (9-2) \times180 \\\\Nonagon = 7 \times180[/tex]

Nonagon = 1260°

Substituting the given parameters into the formula, we have;

[tex]138+154+ 145+ 132+ 128+ 147 + 130+a+a = 1260\\\\974 + 2a = 1260\\\\2a = 1260-974\\\\2a = 286\\\\a = \frac{286}{2}[/tex]

a = 143°

Read more: https://brainly.com/question/23754522

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