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.(1 point)
Responses

24°
24°

56°
56°

40°
40°

20°

Answer 1

Opposite angles in an inscribed quadrilateral are supplementary, so
(x + 16) + (6x − 4) = 180
7x + 12 = 180 → 7x = 168 → x = 24.

Smaller angle = x + 16 = 24 + 16 = 40°.