1. Given a regular octagon, find the measures of the angles formed by (a) two consecutive radii and (b) a radius and a side of the polygon. a. 40°; 230° b. 45°; 67.5° c. 72°; 252° d. 36°; 216°

(B)45°, 67.5°

Step-by-step 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°.

y > 1/3x

y < = -x + 4

hope this : )

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: