UVWX is a square. ZYW and VYX are straight lines. VU = VZ and ∠YVZ = 13°. Find
- ∠VUZ
- ∠XWZ
.
(a)
∠UVX = 45° (Right angle)
∠UVZ
= ∠UVX - ∠YVZ
= 45° - 13°
= 32°
∠VUZ
= (180° - ∠UVZ) ÷ 2
= (180° - 32°) ÷ 2
= 148° ÷ 2
= 74° (Isosceles triangle)
(b)
VU = VZ = VW
ZVW is an isosceles triangle.
∠VZW = ∠VWZ (Isosceles triangle)
∠VWZ
= (180° - ∠XVW - ∠YVZ) ÷ 2
= (180° - 45° -13°) ÷ 2
= 122° ÷ 2
= 61°
∠XWZ
= ∠VWX - ∠VWZ
= 90° - 61°
= 29°
Answer(s): (a) 74°; (b) 29°
