Question

9.5) ifm Z WZY - 100º and mZ WXY = 50°, calculate m ZWX. Justify your work with properties or definitions. Note: figure may not be drawn to scale. I​

Answer 1

Answer:

m∠ZWX = 105°

Step-by-step explanation:

Properties of a kite,

1). One diagonal of a kite bisects at least one pair of opposite angles.

2). Diagonals of a kite kite are perpendicular to each other.

In ΔWTZ,

m∠WZT = $\frac{1}{2}(m\angle WZY)$

              = $\frac{1}{2}(100)$

              = 50°

m∠WTZ = 90° [By second property]

m∠WZT + m∠WTZ + m∠ZWT = 180°

50° + 90° + m∠ZWT = 180°

m∠ZWT = 180° - 140°

              = 40°

Similarly, in ΔWTX,

$m(\angle WXT)=\frac{1}{2}(m\angle WXY)$

m(∠WXT) = $\frac{1}{2}(50)$

                = 25°

m(∠WTX) = 90°

m∠WTX + m∠WXT + m∠TWX = 180°

90° + 25° + m∠TWX = 180°

m∠TWX = 180° - 115°

              = 65°

Since, m∠ZWX = m∠ZWT + m∠TWX

Therefore, m∠ZWX = 40° + 65°

                                 = 105°