Question

reviewing central angles and arc measures
use the drop-down menus to complete the statements.
a central angle of circle p is angle
the measure of \\(\widehat{ru}\\) is
drop-down options: stp, tpq, ust

Explanation:

Step1: Identify Central Angle

A central angle has its vertex at the center of the circle (point P here) and its sides as radii. Let's check each option:

• Angle STP: Vertex at T, not P. Not a central angle.
• Angle TPQ: Vertex at P, sides PT and PQ (radii). So this is a central angle.
• Angle UST: Vertex at S, not P. Not a central angle.

Step2: Measure of Arc RU

The measure of an arc is equal to the measure of its central angle. The central angle for arc RU is ∠RPU? Wait, no, looking at the diagram, the central angle for arc RU is ∠UPR? Wait, the diagram shows ∠UPR? Wait, the given angles at P: ∠TPQ is 107°, ∠UPR is 59°? Wait, no, the arc RU: the central angle for arc RU is ∠RPU? Wait, the central angle corresponding to arc RU is the angle at P between R and U, which is given as 59°? Wait, no, let's check the circle. The sum of central angles in a circle is 360°. But for arc RU, the central angle is ∠UPR, which is 59°? Wait, no, the diagram shows at point P, the angle between PU and PR is 59°, so the measure of arc RU is equal to the measure of its central angle, which is 59°? Wait, but let's confirm the first part. The first drop-down: the central angle must have vertex at P. So TPQ has vertex at P, sides PT and PQ (radii), so that's the central angle. Then for arc RU, the central angle is ∠RPU, which is 59°, so the measure of arc RU is 59 degrees.

Answer:

First drop - down: B. TPQ
Second drop - down: 59° (assuming the second drop - down is to select 59°; if the options are numerical, the measure of arc RU is equal to the measure of its central angle, which is 59°)