A,O,B are 3 points on a line segment and C is a point not lying on AOB if angle AOC - Maths - Geometric Proportions

Question

A,O,B are 3 points on a line segment and C is a point not lying on
AOB if angle AOC = 40 and OX ,OY are the internal and external
bisections of angle AOC respectively then angle BOY is ???

Neha Sethi · Accepted Answer

Dear student
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Since ∠AOC=40°So, ∠BOC=∠AOC=180°   [Linear pair]⇒∠BOC=180°-40°⇒∠BOC=140°Since OY is external bisector of ∠AOCSo, ∠COY=∠BOYand ∠BOC=∠COY+∠BOY⇒∠BOC=2∠BOY⇒140°=2∠BOY⇒∠BOY=70°
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A,O,B are 3 points on a line segment and C is a point not lying on AOB if angle AOC = 40 and OX ,OY are the internal and external bisections of angle AOC respectively then angle BOY is ???