The figure is not drawn to scale. It shows a parallelogram EFGH and an isosceles triangle BEH next to it. ∠DHB = 10°. DC and BA are straight lines. Find
- ∠l
- ∠j + ∠k
- ∠k
(a)
∠l
= 180° - ∠DHB
= 180° - 10°
= 170° (Angles on a straight line)
(b)
∠j = ∠EHG (Parallelogram)
∠j + ∠k
= 180° - 10° - 59°
= 111° (Angles on a straight line)
(c)
∠BEH = ∠j (Corresponding angles)
∠BEH = ∠HBE (Isosceles triangle)
∠j
= 180° - (∠j + ∠k)
= 180° - 111°
= 69°
∠k
= 180° - ∠j - ∠j
= 180° - 69° - 69°
= 42° (Angles sum of triangle)
Answer(s): (a) 170°; (b) 111°; (c) 42°