From the kite ABCD, ∠ABD = 65° and ∠CBD = 46°
Properties of a kite:
- Pair of adjacent sides are equal
- One pair of opposite angle is equal
- Diagonals are perpendicular to each other
- The longer diagonals bisect the other diagonal.
∠ABC≅∠ADC
∠EDC = 180 - 90 - 44 (sum of angle in a triangle)
∠EDC = 46°
∠EDC ≅∠EBC
∠ADE = 180 - 25 - 90 (sum of angle in a triangle)
∠ADE = 65°
∠ADE ≅ ∠ABD(Base angle of isosceles triangle)
Therefore,
∠ABD = 65°
∠EDC ≅ ∠CBD (Base angle of isosceles triangle)
Therefore,
∠CBD = 46°
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