PQRS is a square. GFR and QFS are straight lines. QP = QG and ∠FQG = 13°. Find
- ∠QPG
- ∠SRG
.
(a)
∠PQS = 45° (Right angle)
∠PQG
= ∠PQS - ∠FQG
= 45° - 13°
= 32°
∠QPG
= (180° - ∠PQG) ÷ 2
= (180° - 32°) ÷ 2
= 148° ÷ 2
= 74° (Isosceles triangle)
(b)
QP = QG = QR
GQR is an isosceles triangle.
∠QGR = ∠QRG (Isosceles triangle)
∠QRG
= (180° - ∠SQR - ∠FQG) ÷ 2
= (180° - 45° -13°) ÷ 2
= 122° ÷ 2
= 61°
∠SRG
= ∠QRS - ∠QRG
= 90° - 61°
= 29°
Answer(s): (a) 74°; (b) 29°