NPQR is a square. GFQ and PFR are straight lines. PN = PG and ∠FPG = 13°. Find
- ∠PNG
- ∠RQG
.
(a)
∠NPR = 45° (Right angle)
∠NPG
= ∠NPR - ∠FPG
= 45° - 13°
= 32°
∠PNG
= (180° - ∠NPG) ÷ 2
= (180° - 32°) ÷ 2
= 148° ÷ 2
= 74° (Isosceles triangle)
(b)
PN = PG = PQ
GPQ is an isosceles triangle.
∠PGQ = ∠PQG (Isosceles triangle)
∠PQG
= (180° - ∠RPQ - ∠FPG) ÷ 2
= (180° - 45° -13°) ÷ 2
= 122° ÷ 2
= 61°
∠RQG
= ∠PQR - ∠PQG
= 90° - 61°
= 29°
Answer(s): (a) 74°; (b) 29°
