Parallelogram abcd is a rhombus with m∠ebc=36°. rhombus abcd. point e is at the intersection of the diagonals bd and ac. what is the m∠dae?

Properties of a rhombus:
1. the all sides are equal
2. opposite angles are equal
3. consecutive angles are supplementary
4. The diagonals bisect the angles.
5. The diagonals are perpendicular bisectors of each other.
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∵ abcd is a rhombus:

∴ ∠ abc = 2 ∠ebc = 2 * 36° = 72°  ⇒⇒⇒ property number (4)

∴ ∠ dab = 180 - ∠abc = 180° - 72° = 108° ⇒⇒⇒ property number (3)

∴ ∠ dae = 108°/2 = 54° ⇒⇒⇒ property number (4)


See the attached figure.