Answer:
Hi my dream princess
A regular polygon with an interior angle of 172° has the following characteristics:
Exterior angle: 360° / number of sides - interior angle.
Number of sides: 360° / exterior angle.
Using this information, we can find the exterior angle and the number of sides:
Exterior angle: 360° / number of sides - 172°.
Number of sides: 360° / (360° / number of sides - 172°).
Solving for the number of sides, we have:
Number of sides: 360° / (360° / number of sides - 172°)
= 360° / (360° / number of sides) - 172° / (360° / number of sides)
= number of sides - 172° / (360° / number of sides)
= number of sides (1 - 172° / 360°)
= number of sides * 188° / 360°.
Since we have a fraction involving a fraction, we can simplify:
Number of sides = number of sides * 188° / 360°
= number of sides * 47° / 90°
= number of sides * 47 / 90.
Since 47 and 90 are both divisible by 47, we can simplify further:
Number of sides = number of sides * 47 / 90
= number of sides * 1 / 2.
Therefore, the regular polygon has 2 sides and each exterior angle is 180°. The polygon is an isosceles triangle.