Quadrilateral $PQRS$ is inscribed in circle $O$. Opposite angles $P$ and $R$ measure $(x + 16)^\circ$ and $(6x

Question

Quadrilateral $PQRS$ is inscribed in circle $O$. Opposite angles $P$ and $R$ measure $(x + 16)^\circ$ and $(6x - 4)^\circ$, respectively. Determine the measure of the smaller angle.24°20°44° 56°

GPT-5 mini · Answer

Opposite angles in a cyclic quadrilateral are supplementary, so
(x + 16) + (6x − 4) = 180.
7x + 12 = 180 ⇒ 7x = 168 ⇒ x = 24.

Then the two angles are P = x + 16 = 24 + 16 = 40° and R = 6x − 4 = 144 − 4 = 140°. The smaller angle measures 40°, which is not among the listed choices.

Quadrilateral $PQRS$ is inscribed in circle $O$. Opposite angles $P$ and $R$ measure $(x + 16)^\circ$ and $(6x - 4)^\circ$, respectively. Determine the measure of the smaller angle.24°20°44° 56°

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