Question

Quadrilateral PQRS is inscribed in circle O . Opposite angles P and R measure (x+16)° and (6x−4)° , respectively. Determine the measure of the smaller angle.

Answer 1

Since opposite angles in an inscribed quadrilateral are supplementary, we can set up an equation to find the measure of the smaller angle:

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

Combine like terms:

7x + 12 = 180

Subtract 12 from both sides:

7x = 168

Divide by 7:

x = 24

Now we can find the measure of the smaller angle:

x + 16 = 24 + 16 = 40°

Therefore, the measure of the smaller angle is 40°.