Find the area of the shaded portion in the square.
(assuming the central point of each arc is the corresponding corner)

The area of the shaded = 8 - 2π units²

Step-by-step explanation:

The area of the shaded portion = area square - area not shaded portion

Not shaded portion consists of two equal segments

∵ The side of the square = the radius of the circle = 2

∵ The measure of each angle of the square = π/2 (90° = π/2 rad)

∵ Area each segment = Area sector - area triangle

∵ Area triangle = 1/2 × (2) × (2) = 2 units²

∵ Area sector = (1/2)r²Ф ⇒ r = 2 , Ф = π/2

∴ Area sector = (1/2) (2)² (π/2) = π units²

∴ Area each segment = π - 2

∴ Area not shaded = 2(π - 2) = 2π - 4 units² ⇒ two segment

∵ Area square = 2 × 2 = 4 units²

∴ Area shaded portion = 4 - (2π - 4) = 4 - 2π + 4

                                      = 8 - 2π units²

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.