Question

A student is building a diamond-shaped kite in his science class. To construct the kite, the student has assembled four congruent right triangle pieces of fabric to form the diamond. The diagonals of the kite are perpendicular to one another. If angle ABC on the side of the kite is 2004-02-02-01-00_files/i0310000.jpg, what will angle BCD on the tail end of the kite be? 

Answer 1

Δ CBE is a right triangle.
∠EBC = 1/2 ∠ ABC = 1/2 · 116° = 58°
∠EBC + ∠ECB = 90°
∠ECB = 90° - 58° = 32°
∠DCB = 2 · 32° = 64°
Answer: c ) 64