line AB and CD intersect each other at 'O'. ∠AOC = 130°. Find the reflex angle of ∠BOC.
A190°
B120°
C310°
D240°
Answer:
C. 310°
Read Explanation:
Solution: Given: ∠AOC = 130° Concept: The sum of angles drawn on a straight line is 180° is called linear pairs of angles. Reflex angle: An angle greater than 180° and less than 360°. Calculation: ∠AOC = 130° ⇒ ∠AOC = (2x + 90)° = 130° ⇒ 2x = 40° ⇒ x = 20° (x + y) + (2x + 90) = 180° (Linear pair of angles) ⇒ (20° + y) + 130° = 180° ⇒ y = 30° ∠BOC = x + y ⇒ ∠BOC = 20° + 30° = 50° Reflex angle of ∠BOC = 360° - 50° ∴ Reflex angle of ∠BOC = 310° The correct option is 3 i.e. 310° Shortcut Trick ∠AOC + ∠BOC = 180° ----(By linear pair) ⇒ 130° + ∠BOC = 180° ⇒ ∠BOC = 50° Reflex angle of ∠BOC = 360° - 50° ∴ Reflex angle of ∠BOC = 310°