Find the measures of the angles formed by (a) two consecutive radii and (b) a radius and a side of a regular dodecagon.

A regular dodecagon is a regular polygon, and it as all its sides to be congruent.

(a) The angle formed by two consecutive radii

So, the angle between consecutive radii is:

Hence, the angle formed by two consecutive radii is 30 degrees

(b) The angle formed by a radius and the side of a regular dodecagon

The triangle in one part of a regular dodecagon is a isosceles triangle.

The required angle is the base angle of the triangle.

And it is calculated using:

This gives

Subtract 30 from both sides

Divide both sides by 2

Hence, the angle formed by a radius and the side of a regular dodecagon is 75 degrees

Read more about regular polygons at:

link

(d)

step-by-step explanation:

given: the line in the graph passes through points (5,30) and (6,26).

then, the equation of line is:

now, put y=a(n) and x=n,

hence, option d is correct.

d

step-by-step explanation:

given

y + 3 = - 4(x - 2) ← distribute the parenthesis

y + 3 = - 4x + 8 ( subtract 3 from both sides )

y = - 4x + 5 → d