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 116, what will angle BCD on the tail end of the kite be?
a.32
b.58
c.64
d.90
The total angle of this four-sided kite is 360° = ∠ABC + ∠ADC + ∠BAD + ∠BCD. We know that ∠ABC = ∠ADC and ∠BAD = ∠BCD, so we can substitute values into the equation. We let x = ∠BAD = ∠BCD. The equation becomes 360° = 116° + 116° + 2x. Solving for x gives us a value of 64° for ∠BCD.
