Five rays OA, OB, OC, OD and OE all start from point O. Angles AOB, BOC, COD and DOE are all equal. Angle EOA = 40°. Find the size of angle BOD.
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Worked Solution
Step 1: Let each of the four equal angles be x°.
The five angles at point O sum to 360°:
4x + 40 = 360
Step 2: Solve for x.
4x = 360 − 40 = 320
x = 320 ÷ 4 = 80°
Step 3: Angle BOD spans two of the equal angles (angle BOC and angle COD).
Angle BOD = x + x = 80 + 80 = 160°
Answer: 160°
Correct answer: 160°
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