Answer :
a). The angle m∠VXU = 57.5° is an inscribed angle.
b). Arc WX = 65° is a minor arc.
c). The arc VWX form a semicircle with the diameter VX.
d). The measure of the arc VWX is equal to 180°
e). The measure of the central angle m∠VUW is equal to 115°.
The central angle of a circle subtends an arc with a measure equal to the angle itself, while the inscribed angle subtends an arc with a measure twice its own.
a). The angle m∠VXU at the circle circumference subtends the arc VW hence it is an inscribed angle so;
m∠VXU = 115°/2 = 57.5°
b). The arc WX is a minor arc compared to the arc VW, and its measure is:
arc WX = 180° - 115° = 65° {supplementary angles}
c). The arc VWX form is a semicircle as it is enclosed by the diameter VX.
d). arc VWX = arc WV + arc WX
arc VWX = 115° + 65°
arc VWX = 180°
e). The central m∠VUW have the same measure with the measure of the arc WX it subtends, hence;
m∠VUW = 115°.
Therefore, for the circle U, angle m∠VXU = 57.5° is an inscribed angle, arc WX = 65° is a minor arc, arc VWX form a semicircle, arc VWX = 180° and m∠VUW = 115°.
