Figure ABCD is a rhombus, and m∠AEB = 7x + 6. Solve for x.
Rhombus ABCD with diagonals AC and BD and point E as the point of intersection of the diagonals.
5.56
12
24.85
Not enough information
Since ABCD is a rhombus, we know that the diagonals are perpendicular bisectors of each other. This means that m∠AEB = m∠DEB. Therefore, we can set up an equation as follows:
7x + 6 = m∠DEB
Since the sum of the angles in a quadrilateral is 360 degrees, we can also say:
m∠AEB + m∠DEB = 360
Substitute the given value for m∠AEB and the equation from above into the second equation:
7x + 6 + 7x + 6 = 360
14x + 12 = 360
14x = 348
x = 24.85
Therefore, x = 24.85. The answer is 24.85.