Question

Quadrilateral PQRS
𝑃
𝑄
𝑅
𝑆
is inscribed in circle O
𝑂
. Opposite angles P
𝑃
and R
𝑅
measure (x+16)°
(
𝑥
+
16
)
°
and (6x−4)°
(
6
𝑥
−
4
)
°
, respectively. Determine the measure of the smaller angle.(1 point)
Responses

56°
56°

24°
24°

20°
20°

40°

Answer 1

Since opposite angles in a cyclic quadrilateral sum to 180°:
(x + 16) + (6x − 4) = 180
7x + 12 = 180 → 7x = 168 → x = 24.

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