Question

The diagonals of rhombus ABCD intersect at E. Given that m/BAC = 53°, DE = 8, and EC = 6, find

m/AED.
A
53°
8 E 6
m/AED=

Answer 1

The measure of angle AED in rhombus ABCD, where the diagonals intersect at E, is 90°, as triangle AED is a right triangle with DE and EC being the legs.

Step-by-step explanation:

The diagonals of a rhombus intersect at a point that bisects each of the diagonals, and the angles opposite each other are equal.

Since we know that m/BAC = 53°, the angle m/DAC is also 53° because they are opposite angles created by the intersection of the diagonals.

In a rhombus, the diagonals perpendicularly bisect each other.

Thus, triangle AED is a right triangle with angle m/AED being the right angle.

A right angle measures 90°, so m/AED = 90°.