Respuesta :
Answer:
45.
Step-by-step explanation:
Each exterior angle = 180 - 172 = 8 degrees.
Since the total of the exterior angles = 360 the number of sides =
360 / 8
= 45 sides.
NOTE: the total of exterior angles of all polygons = 360 degrees.
The polygon which has 172 degrees as measure of all of its interior angles has in total 45 sides.
Given that:
Measure of each angle of the polygon = 172 degree.
Let there be n sides in the polygon.
The exterior and interior angles are supplementary, which means:
Exterior angle = 180 degrees - interior angle = 180 - 172 = 8 degrees.
Now, since it is a theorem that:
"The sum of all exterior angles of a regular polygon is 360 degrees."
Thus, we have:
[tex]8 \times n = 360\\\\n = \dfrac{360}{8}\\\\n = 45[/tex]
Thus, there are total 45 sides in the given polygon.
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