Acircle is inscribed in a square. the area of the circle is 507 square inches. what is the length of each side of the square? use 3 for pi.

26 inches

Step-by-step explanation:

We are given;

We are given the area as 507 square inches

But;

Area of the circle = pi × r²

Thus we can get the radius of the circle;

Thus;

507 in² = 3 × r²

r² = (507 ÷ 3)

   = 169

r =√169

  = 13 inches

But, Diameter = 2 r

Thus; Diameter = 2 × 13

                        = 26 inches

But, in this case, diameter = side of the square

Therefore, the side of the square is 26 inches

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.