LMNP is a square. ZYN and MYP are straight lines. ML = MZ and ∠YMZ = 13°. Find
- ∠MLZ
- ∠PNZ
.
(a)
∠LMP = 45° (Right angle)
∠LMZ
= ∠LMP - ∠YMZ
= 45° - 13°
= 32°
∠MLZ
= (180° - ∠LMZ) ÷ 2
= (180° - 32°) ÷ 2
= 148° ÷ 2
= 74° (Isosceles triangle)
(b)
ML = MZ = MN
ZMN is an isosceles triangle.
∠MZN = ∠MNZ (Isosceles triangle)
∠MNZ
= (180° - ∠PMN - ∠YMZ) ÷ 2
= (180° - 45° -13°) ÷ 2
= 122° ÷ 2
= 61°
∠PNZ
= ∠MNP - ∠MNZ
= 90° - 61°
= 29°
Answer(s): (a) 74°; (b) 29°
