Question

N.8 Properties of rhombuses QVX Quadrilateral DEFG is a rhombus and angle FEG =7v. What is the value of v ?

Answer 1

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:

1. Angle FEG = 7v
2. Angle FEG + Angle EFG + Angle EFG + Angle EFD = 360 degrees
3. 7v + 90 + 90 + 7v = 360 degrees
4. 14v + 180 = 360 degrees
5. 14v = 180 degrees
6. v = 180 / 14
7. v = 12.857 degrees (rounded to three decimal places)

Thus, the value of v in the problem is approximately 12.857 degrees.