quadrilateral PQRS is inscribed in circle O. Opposite angles P and R measure (x+16) degrees and (6r-4) degrees, respectively. determine the measure of the smaller angle the answer HAS TO BE either 40 degrees,24 degrees,20 degrees or 56 degrees
To determine the measure of angle P and R in quadrilateral PQRS, we note that opposite angles in an inscribed quadrilateral are supplementary.
Therefore, we have:
Angle P + Angle R = 180 degrees
(x + 16) + (6r - 4) = 180
Simplifying, we get:
x + 6r + 12 = 180
x + 6r = 168
Given that x + 16 and 6r - 4 are opposite angles, they must add up to 180 degrees:
(x + 16) + (6r - 4) = 180
x + 6r + 12 = 180
x + 6r = 168
Now we have a system of equations:
x + 6r = 168
x + 6r = 168
Subtracting the two equations, we get:
0 = 0
This means that the system of equations has infinitely many solutions and we cannot determine a unique value for x and r. Therefore, we cannot determine the exact measure of angles P and R in this case.
Since we are unable to determine the measure of the smaller angle, none of the provided options (40 degrees, 24 degrees, 20 degrees, or 56 degrees) can be selected as the answer.