2020 · Q97
In the given figure AB is parallel to CD and AC is parallel to BD. If ∠EAC = 40°, ∠FDG = 55°, ∠HAB = x°, then what is the value of x?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A85°
- B80°
- C75°
- D65°
Explanation
∠FDG = 55° gives the vertical angle ∠CDB = 55°. AC ∥ BD with transversal CD gives ∠ACD = 180° − 55° = 125°; AB ∥ CD with transversal AC gives ∠CAB = 180° − 125° = 55°. H, A, E are collinear, so x = 180° − ∠EAC − ∠CAB = 180° − 40° − 55° = 85.