Question

Quadrilateral UVWX is a kite. What is mZw?

Answer 1

m∠W = 80°

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°

Answer 2

• 80°

Explanation:

According to properties of the kite, it has one pair of congruent opposite angles:

• m∠U = m∠W

We have two angle measures given and the sum of interior angles is 360:

• m∠U + m∠W + m∠X + m∠V = 360
• 2*m∠W + 116 + 84 = 360
• 2*m∠W + 200 = 360
• 2*m∠W = 160
• m∠W = 80