2020 · Q96
In the given figure PQ is parallel to RS, ∠AEF = 95°, ∠BHS = 110°, and ∠ABC = x°. Then what is the value of x?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A15
- B25
- C30
- D35
Explanation
At E, ∠AEF = 95°; its vertical angle ∠BEP = 95°, so line AB meets the vertical at 95° — i.e. it is inclined 5° to the horizontal, descending to the right. At H, ∠BHS = 110°, so line CB meets the vertical at 110° — inclined 20° to the horizontal, ascending to the right. At B, ray BA therefore points 5° above the leftward horizontal while ray BC points 20° below it. Hence x = 5° + 20° = 25.