Respuesta :
Answer:
72°
Step-by-step explanation:
The required angle of rotation can be found by considering the regular polygon to be inscribed in a circle. Each of its 10 vertices will be separated by a central angle of 360°/10 = 36°. So, the vertices a8 and a4 will be separated by a central angle of (8 -4)(36°) = 144°.
The angle a4-a1-a8 is an inscribed angle, so will have half the measure of the central angle intercepting the a4-a8 arc. The desired angle of rotation to map a4 to a8 is ...
α = 144°/2 = 72°
The value of angle α is 72° if the regular polygon is inscribed in a circle and rotation centered at a_1
What is a regular polygon?
A polygon is a geometric figure with a finite number of sides in two dimensions. A polygon's sides or edges are made up of straight-line segments that are joined end to end to form a closed shape. The vertices or corners are the points where two line segments meet, and an angle is generated as a result.
Consider the regular polygon to be inscribed in a circle to get the required angle of rotation.
A center angle of 360°
=360°/10 = 36°
It will separate each of its 10 vertices.
The central angle:
= (8 - 4)×(36°) = 144°
An inscribed angle is a4-a1-a8:
So α will be:
α = 144/2 ⇒ 72°
Thus, the value of angle α is 72° if the regular polygon is inscribed in a circle and rotation centered at a_1
Learn more about the regular polygon here:
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