In kite WXYZ, mZWY = 41° and mXYW = 11° What is mWZY?

Question

asked Dec 14, 2022 82.1k views

1 Answer

Matthew Kime · Answer 1 · 2022-12-19T14:30:50+0000

Answer:

128°

Explanation:

In kite WXYZ, WY and XZ are longer and smaller diagonals respectively.

Longer diagonal bisects the opposite angles.

$\therefore m\angle ZYW =m\angle XYW$

$\because m\angle XYW = 11\degree... (given)$

$\therefore m\angle ZYW =11\degree$

$In\: \triangle WYZ$

$m\angle ZYW + m\angle ZWY + m\angle WZY=180\degree$

$11\degree + 41\degree+ m\angle WZY=180\degree$

$52\degree+ m\angle WZY=180\degree$

$m\angle WZY=180\degree - 52\degree$

$\purple{\bold {m\angle WZY=128\degree}}$