Answer:
(B)45°, 67.5°
Explanation:
A regular polygon is a polygon in which all the sides are equal.
An Octagon is a polygon with 8 sides.
Since it is a Regular polygon, the following holds:
1.The Radii are equal
2. The angle Subtended by two radii are equal for all triangles in the octagon.
3. There are 8 Isosceles triangles in the octagon.
(a)Measures of angle formed by Two radii
From the centre of the octagon, there are 8 equal angles.
Sum of Angle at a point= 360°
Each Angle=360°÷ 8 = 45°
The measures of angle formed by two radii is 45°.
(b)a radius and a side of the polygon.
Since the triangles are Isosceles, the base angles at the side of the octagon are equal.
Let x be the angle made by a radius with a side.
From (a) above,
x+x+45°=180°(Sum of Angle in a Triangle)
2x=180-45°
2x=135°
x=135°÷2=67.5°
The angle between a radius and a side of the polygon is 67.5°.
Explanation: