The figure is a regular hexagon, where each interior angle measures 120 degrees.
Angle RVU is an interior angle of the hexagon, so it also measures 120 degrees.
Therefore, the correct answer is 240° which is not there among the options.
The measure of angle RVU is 240° .
Step 1: Identify the relevant angles
We are asked to find the measure of angle RVU.
We are given that the figure is a regular hexagon.
Step 2: Recall the properties of regular hexagons
Each interior angle of a regular hexagon measures 120 degrees.
The sum of the interior angles of a hexagon is 720 degrees.
Step 3: Apply the properties to the figure
Since QR is a side of the hexagon, angle QRU and angle VRU are interior angles of the hexagon.
As each interior angle of a regular hexagon measures 120 degrees, we know that:
angle QRU = 120 degrees
angle VRU = 120 degrees
Step 4: Find angle RVU
Angle RVU is formed by the intersection of two interior angles of the hexagon, QRU and VRU.
Since these angles are adjacent, their sum is equal to the angle between their non-adjacent sides (angle QVU).
Step 5: Calculate angle QVU
To find angle QVU, we can use the fact that the sum of the interior angles of a hexagon is 720 degrees.
We already know that two of the interior angles (QRU and VRU) each measure 120 degrees.
Therefore, the sum of the remaining four interior angles is:
720 degrees - 120 degrees - 120 degrees = 480 degrees
Step 6: Divide the remaining angles equally
Since the remaining four interior angles are congruent (the hexagon is regular), each must measure:
480 degrees / 4 = 120 degrees
Therefore, angle QVU also measures 120 degrees.
Step 7: Conclusion
We found that angle QRU = 120 degrees, angle VRU = 120 degrees, and angle QVU = 120 degrees.
Since angle RVU is formed by the intersection of angles QRU and VRU, and these angles are adjacent, we can conclude that:
angle RVU = 120 degrees + 120 degrees = 240 degrees
Therefore, the measure of angle RVU is 240 degrees. The correct answer is not listed among the options provided.