Answer:
m∠W = 80°
Step-by-step explanation:
Properties of a kite:
- Quadrilateral (two-dimensional shape with 4 sides)
- Two pairs of consecutive equal sides
- Diagonals are perpendicular to each other
- The longer diagonal bisects the shorter diagonal
- One pair of opposite angles are equal
- Interior angles sum to 360°
- Area is half the product of its diagonals
As the interior angles of a kite sum to 360°:
⇒ m∠U + m∠V + m∠W + m∠X = 360°
⇒ m∠U + 84° + m∠W + 116° = 360°
⇒ m∠U + m∠W + 200° = 360°
⇒ m∠U + m∠W = 160°
As one pair of opposite angles are equal, and from inspection of the given kite, opposite angles X and V are not equal, this means that angles U and W are equal.
⇒ m∠U + m∠W = 160°
⇒ 2m∠W = 160°
⇒ m∠W = 80° and m∠U = 80°
