Respuesta :

Answer:

45° and 135°

Step-by-step explanation:

(a)

The sum of the angles around O = 360°

There are 8 segments from each vertex to O , thus

∠ AOB = 360° ÷ 8 = 45°

The sum of the interior angles of a regular polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 8 , then

sum = 180° × 6 = 1080°

In a regular polygon the 8 interior angles are equal, thus

∠ ABC = 1080 ÷ 8 = 135°

sqdancefan

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Answer:

  a) angle AOB = 45°

  b) angle ABC = 135°

Step-by-step explanation:

a) The sum of the 8 identical central angles is 360°, so each one has a measure of ...

  angle AOB = 360°/8 = 45°

__

b) The sum of the 8 exterior angles is 360°, so each one is 45°, the same measure as the central angle. The measure of angle ABC is the supplement of the exterior angle at B, so is ...

  angle ABC = 180° -45° = 135°

_____

In the attached image, the central point is your O. Angle AOB is the interior angle of triangle AOB whose vertex is at O.

Ver imagen sqdancefan

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