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?
1 answer:
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 <span>a rhombus:
</span>
<span>∴ ∠ abc = 2 ∠ebc = 2 * 36° = 72° ⇒⇒⇒ property number (4)
</span>
<span>∴ ∠ dab = 180 - ∠abc = 180° - 72° = 108° </span><span>⇒⇒⇒ property number (3)
</span>
∴ ∠ dae = 108°/2 = 54° <span>⇒⇒⇒ property number (4)
</span><span>
</span><span>
</span><span>See the attached figure.</span>
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.
==================================================
∵ abcd is <span>a rhombus:
</span>
<span>∴ ∠ abc = 2 ∠ebc = 2 * 36° = 72° ⇒⇒⇒ property number (4)
</span>
<span>∴ ∠ dab = 180 - ∠abc = 180° - 72° = 108° </span><span>⇒⇒⇒ property number (3)
</span>
∴ ∠ dae = 108°/2 = 54° <span>⇒⇒⇒ property number (4)
</span><span>
</span><span>
</span><span>See the attached figure.</span>
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