Question

1. John is making a kite based on the pattern below. About how much binding does John need to cover the edges of the kite?


2. In kite ABCD, m∠EBC=36°. Identify m∠BCD.


3. In kite ABCD, m∠ADE=54°. Identify m∠DAE.

Answer 1

The kite is a geometric figures that have diagonals that are perpendicular.

The correct responses are;

• 1. About 40.6 in.

• 2. m∠BCD is 54°

• 3. m∠DAE is 36°

Reasons:

1. The length of the binding is given by Pythagoras's theorem as follows;

Length of binding = 2 × (√(15² + 3²) + √(3² + 4²)) ≈ 40.6

The length of binding John needs is about 40.6 in.

2. m∠EBC = 36°

The angles formed at the intersection of the diagonals are 90°

Therefore, by angles formed in right triangle ΔCBE, b and m∠BCD

are complementary angles.

Which gives;

m∠BCD = 90° + 36° = 54°

• m∠BCD = 54°

3. m∠ADE = 54°

Given that m∠ADE and m∠DAE are the acute angles in the right triangle ΔADE, we have;

m∠ADE and m∠DAE are complementary angles.

Which gives;

m∠ADE + m∠DAE = 90°

m∠DAE = 90° - m∠ADE

Which gives;

m∠DAE = 90° - 54° = 36°

• m∠DAE = 36°

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