The figure is not drawn to scale. QR//TS and SR//UQ. Triangles QUR and RST are isosceles triangles. Find
- ∠j
- ∠k.
(a)
∠RST = ∠RQU = 72° (SR//UQ, RQ//ST)
∠QRU
= (180° - 72°) ÷ 2
= 108° ÷ 2
= 54° (Isosceles triangle)
∠SRT
= 180° - 72° - 72°
= 36° (Isosceles triangle)
∠j
= 180° - 72° - 54° - 36°
= 18° (Interior angles, RQ//ST)
(b)
∠k
= 180° - 26° - 18°
= 136° (Angles sum of triangle)
Answer(s): (a) 18°; (b) 136°