In a trapezium, BANK, BO and OA bisect angle A and angle B respectively. If angle OBA =55° and angle OAB = 65°, find angle BOA, angle BNK and angle ANK? Also draw the figure. Please answer. I will mark correct answer as brainliest. Please fast.
Answers
Given : BANK, BO and OA bisect angle A and angle B respectively.
angle OBA =55° and angle OAB = 65°,
To find : angle BOA, angle BKN and angle ANK
Solution:
Refer the attached figure for solution :
∠OBA =55°
∠ OAB = 65°
In a triangle sum of angles = 180°
=> ∠OBA + ∠OAB + ∠BOA = 180°
=> 55° + 65° + ∠BOA = 180°
=> ∠BOA = 60°
BO and OA bisect angle A and angle B
∠OBA =55° = ∠OBK => ∠ABK = ∠OBA + ∠OBK = 110°
∠ OAB = 65° = ∠ OAN => ∠BAN = ∠OAB + ∠OAN = 130°
As BANK is trapezium Hence BA || NK
=> ∠ABK + ∠BKN = 180°
=> 110° + ∠BKN = 180°
=> ∠BKN = 70°
and ∠BAN + ∠ANK = 180°
=> 130° + ∠ANK = 180°
=> ∠ANK = 50°
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