Respuesta :

Answer:

36

Step-by-step explanation:

In any n sided polygon the sum of interior angles would be

(2n-4)90 degrees

There will be n exterior angles

The sum of interior and exterior would be

=180 n (by linear pair postulate)

Hence sum of exterior angles = (2n-4)90- 180 n=360

Hence in any polygon sum of exterior angles = 360

IN 10 sided polygon, i.e. decagon, sum of exterior angles =360

Hence each exterior angle = angle 1 = 360/10 = 36

abidemiokin

The measure of angle 1 from the given figure is 36 degrees.

Exterior and interior angle of a polygon

In any n sided polygon, the sum of interior angles is expressed as:

  • Sum = (2n-4)90 degrees

This shows that there will be n exterior angles

The sum of interior and exterior = 180n

Get the sum of the exterior angle

  • The sum of exterior angles = (2n-4)90 - 180n = 360
  • The measure of each exterior angle = [tex]\frac{360}{n} [/tex]
  • n is the number of sides = 10

The measure of each exterior angle = [tex]\frac{360}{10} = 36 [/tex]

Hence the measure of angle 1 from the given figure is 36 degrees.

Learn more on exterior angles here; https://brainly.com/question/2546141

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