Final answer:
The value of v for quadrilateral DEFG, which is a rhombus with angle FEG = 7v, is approximately 12.857 degrees after solving the equation for the sum of interior angles in a quadrilateral.
Step-by-step explanation:
The question asks for the value of v given that quadrilateral DEFG is a rhombus and the measure of angle FEG is 7v. In a rhombus, all sides are of equal length, and opposite angles are equal. Since the sum of the interior angles in any quadrilateral is 360 degrees, and a rhombus has two pairs of equal angles, we can deduce that the two angles adjacent to angle FEG must each be 90 degrees as a rhombus has four angles at 90 degrees. Therefore, angles DEF and DEG would both be 90 degrees. Since DEFG is a rhombus, angles EFG and EFG are equal, meaning:
- Angle FEG = 7v
- Angle FEG + Angle EFG + Angle EFG + Angle EFD = 360 degrees
- 7v + 90 + 90 + 7v = 360 degrees
- 14v + 180 = 360 degrees
- 14v = 180 degrees
- v = 180 / 14
- v = 12.857 degrees (rounded to three decimal places)
Thus, the value of v in the problem is approximately 12.857 degrees.