quadrilateral PQRS s 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

Answer 1

Since PQRS is inscribed in circle O, opposite angles are supplementary. Therefore:

(x + 16) + (6r - 4) = 180

Simplify the equation:

x + 16 + 6r - 4 = 180
x + 6r + 12 = 180
x + 6r = 168

Since we are looking for the smaller angle, we need to find the smaller angle which is (6r - 4). Let's solve for r in terms of x:

x + 6r = 168
6r = 168 - x
r = (168 - x) / 6

Now substitute r back into the expression for the smaller angle:

6r - 4 = 6((168 - x) / 6) - 4
= 168 - x - 4
= 164 - x

Therefore, the measure of the smaller angle is 164 - x degrees.