Answer:
a) ∠VUW
b) VY
c) XYV
d) 180°
e) 65°
Explanation:
Part A:
A central angle is an angle that creates an arc in a circle, while also having its vertex as the center of the circle.
Here the center is U. So, the vertex of the angle must include U.
This means that there are multiple answers to part a.
The answers can be:
∠VUW
∠WUX
∠XUV
Part B:
A minor arc is any arc that doesn't exceed 180°.
The possible answers for part b, using this definition are:
WV
VY
XY
Part C:
The answer you inputted here is incorrect.
The order of the letters matter.
A tip for you to never mess these up is to trace the letters you've chosen with your finger and see if that image you make with your finger matches up with the shape you wanted to make.
An arc that makes a semicircle is an arc that connects the endpoints of the diameter. The diameter in this case is VX.
This means that your answer must start with V and end with X, or the other way around. (Meaning you could start with x and end with v, but always make sure you keep the endpoints of the diameter as the endpoints of the arc.)
The possible answers for this part are either:
VYX or VWX
Part D:
This arc intercepts the diameter, which is a straight line and a central angle.
The angle of a diameter is 180°.
The arc of an intercepted central angle has the same measure of the central angle itself.
So, the measure of VWX is 180°.
Part E:
If an arc intercepts a central angle, then the arc has the same measure as the central angle.
This rule works the other way around, too.
So, the central angle has the same measure as the minor arc that it intercepts.
Measure of arc VUW is 65°, so m∠VUW is also 65°.