This is geometry, angles in inscribed quadrilaterals,

Rule: The inscribed quadrilateral inside the circle has the opposite angles add to 180 (aka they are supplementary)

So we'll add up angles R and T, and set that sum equal to 180 like so

R+T = 180

Replace R and T with their respective expressions in terms of x leading to this

(x+9) + (x-11) = 180

Let's solve for x

x+9 + x - 11 = 180

2x - 2 = 180 combine like terms

2x-2+2 = 180+2 ... add 2 to both sides

2x = 182

2x/2 = 182/2   divide both sides by 2

answer

explanation

the area of a circle is calculated using the formula

or

we can use any of the above formulae to calculate the required. preferably, let us use the latter since the diameter is

we substitute the diameter into the formula to get:

this is the exact value for the area of the circle.

the correct answer is a