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

m∠ZWX = 105°

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 =
`(1)/(2)(m\angle WZY)`

=
`(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)=(1)/(2)(m\angle WXY)`

m(∠WXT) =
`(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°