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)
24°
20°
40°
56°

Explanation:

Step1: Use cyclic quadrilateral property

Opposite angles sum to $180^\circ$:
$$(x + 16) + (6x - 4) = 180$$

Step2: Simplify and solve for $x$

Combine like terms and isolate $x$:
$$7x + 12 = 180$$
$$7x = 168$$
$$x = 24$$

Step3: Calculate both angles

Substitute $x=24$ into each angle:
Angle $P$: $24 + 16 = 40^\circ$
Angle $R$: $6(24) - 4 = 140^\circ$

Step4: Identify the smaller angle

Compare the two angle measures.

Answer:

40°