The figure is not drawn to scale. JMPT is a parallelogram. LQS and KNR are triangles. ∠LQR = 81° and RKN = 51°. Find
- ∠KLQ
- the sum of ∠KRN, ∠LGN and ∠NHQ.
(a)
∠KLQ
= 180° - 81°
= 99° (Interior angles, JM//TP)
(b)
∠LGN = ∠KGH (Vertically opposite angles)
∠NHQ = ∠RHG (Vertically opposite angles)
KRHG is a quadrilateral.
∠KRN + ∠RHG + ∠KGH + 51° = 360° (Sum of angles in a quadrilateral)
∠KRN + ∠RHG + ∠KGH
= 360° - 51°
= 309°
Answer(s): (a) 99°; (b) 309°