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Area of the shaded region is 2868.61 square inches.

Solution:

Diameter of the smaller circle = 20.4 in

Radius of the smaller circle = 20.4 ÷ 2 = 10.2 in

Area of the smaller circle = πr²

                                          = 3.14 × (10.2)²

Area of the smaller circle = 326.6856 in²

Radius of the larger circle = (10.2 + 21.7) in = 31.9 in

Area of the larger circle = πR²

                                        =3.14 × (31.9)²

Area of the larger circle = 3195.2954 in²

Area of shaded region = Area of larger circle – Area of smaller circle

                                      = 3195. 2954 in² – 326.6856 in²

                                      = 2868.6098 in²

                                      = 2868.61 in²

Area of the shaded region is 2868.61 square inches.

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180