Lines AB and CD intersect at point O. Ray OE lies between rays OA and OC such that OE bisects angle AOC. Given that angle BOC = (4x − 20)° and angle AOD = (2x + 40)°, find the size of angle EOC.
Show Worked Solution
Worked Solution
Step 1: Angle BOC and angle AOD are vertically opposite, so they are equal.
(4x − 20)° = (2x + 40)°
4x − 2x = 40 + 20
2x = 60
x = 30
Step 2: Find angle BOC.
Angle BOC = 4(30) − 20 = 120 − 20 = 100°
Step 3: Find angle AOC using angles on a straight line.
Angle AOC = 180° − 100° = 80°
Step 4: OE bisects angle AOC, so angle EOC = angle AOC ÷ 2.
Angle EOC = 80° ÷ 2 = 40°
Answer: 40°
Correct answer: 40°
Want more questions like this? Superholic Lab has 10,000+ MOE-aligned questions with full worked solutions.
Start Free Trial — 7 Days Free