9514 1404 393
Answer:
- RV = 35°
- RTV = 325°
- PVR = 180°
- PQ = 115°
Explanation:
The relevant relations are ...
the measure of a semicircle is 180°; a circle is 360°
vertical angles are congruent (have the same measure)
the measures of adjacent arcs add to give the measure of the overall arc
the measure of an arc is the same as the central angle it subtends
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arc RV
Angle RCV is a vertical angle with respect to angle PCT, so has the same measure. It is a central angle, so ...
angle RCV = angle PCT = 35° = arc RV
arc RTV
Arc RTV is arc RV the long way around. Its measure is the difference between 360° (a full circle) and short arc RV:
arc RTV = 360° -35° = 325°
arc PVR
Arc PVR is a semicircle.
arc PVR = 180°
arc PQ
Arc PQR is a semicircle, so is 180°. Arc QR is shown as 65°, so arc PQ is the difference:
arc PQ = 180° -65° = 115°