In the figure, EFGH is a parallelogram. O is the centre of the circle. Find
- ∠EHG
- ∠EFH
(a)
∠OFH = ∠FHO = 40° (Angle properties within a circle)
∠HOF
= 180° - 40° - 40°
= 100° (Angles sum of triangle)
∠OEF + ∠OFE = ∠FOH (Exterior angle of a triangle)
∠OEF = ∠OFE (Isosceles triangle, OE = OF)
∠OEF
= 100° ÷ 2
= 50° (Exterior angle of a triangle)
∠EHG
= 180° - 50°
= 130° (Interior angles)
(b)
∠EFH
= 180° - 50° - 40°
= 90° (Angle sum of triangles)
Answer(s): (a) 130°; (b) 90°