Question
In kite ABCD, find the measure of ∠BAO.
- 180°
- 90°
- 54°
- 36°
Hint:
A kite is a quadrilateral that has 2 pairs of equal-length sides and these sides are adjacent to each other.
Properties:
- The two angles are equal where the unequal sides meet.
- It can be viewed as a pair of congruent triangles with a common base.
- It has 2 diagonals that intersect each other at right angles.
- The longer or main diagonal bisects the other diagonal.
- A kite is symmetrical about its main diagonal.
- The shorter diagonal divides the kite into 2 isosceles triangles.
The correct answer is: 54°
A kite is a quadrilateral that has 2 pairs of equal-length sides and these sides are adjacent to each other.
Properties:
- The two angles are equal where the unequal sides meet.
- It can be viewed as a pair of congruent triangles with a common base.
- It has 2 diagonals that intersect each other at right angles.
- The longer or main diagonal bisects the other diagonal.
- A kite is symmetrical about its main diagonal.
- The shorter diagonal divides the kite into 2 isosceles triangles.
The diagonals of a kite are perpendicular.
∠AOB = 90
In ΔAOB,
∠BAO = 180° - ∠AOB - ∠ABO [Angle sum property]
= 180° - ∠AOB - 36°
= 54°
Thus, the measure of ∠BAO is 54°.
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