In the figure, PQRS is a quadrilateral where ∠PQR = 135° and ∠QRS = 112°. ∠RST = 81° and QR = RS. The point T on PS is such that QT is parallel to RS. Calculate
- ∠QST
- ∠QPT
(a)
∠RSQ
= (180° - 112°) ÷ 2
= 34° (Isosceles triangle)
∠QST
= 81° - 34°
= 47°
(b)
∠QPT
= 360° - 112° - 81° - 135°
= 32° (Sum of angles in a quadrilateral)
Answer(s): (a) 47°; (b) 32°