The figure is not drawn to scale. JMPT is a parallelogram. LQS and KNR are triangles. ∠LQR = 83° and RKN = 55°. Find
- ∠KLQ
- the sum of ∠KRN, ∠LGN and ∠NHQ.
(a)
∠KLQ
= 180° - 83°
= 97° (Interior angles, JM//TP)
(b)
∠LGN = ∠KGH (Vertically opposite angles)
∠NHQ = ∠RHG (Vertically opposite angles)
KRHG is a quadrilateral.
∠KRN + ∠RHG + ∠KGH + 55° = 360° (Sum of angles in a quadrilateral)
∠KRN + ∠RHG + ∠KGH
= 360° - 55°
= 305°
Answer(s): (a) 97°; (b) 305°