The figure is not drawn to scale. HLNS is a parallelogram. KPR and JMQ are triangles. ∠KPQ = 75° and QJM = 56°. Find
- ∠JKP
- the sum of ∠JQM, ∠KFM and ∠MGP.
(a)
∠JKP
= 180° - 75°
= 105° (Interior angles, HL//SN)
(b)
∠KFM = ∠JFG (Vertically opposite angles)
∠MGP = ∠QGF (Vertically opposite angles)
JQGF is a quadrilateral.
∠JQM + ∠QGF + ∠JFG + 56° = 360° (Sum of angles in a quadrilateral)
∠JQM + ∠QGF + ∠JFG
= 360° - 56°
= 304°
Answer(s): (a) 105°; (b) 304°