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if the angle bisectors of triangle abc intersect at x,y,z. then prove that the measure of the angles of triangle abc are 90-1/2of a, 90-1/2 of b, 90-1/2 of c

if the angle bisectors of triangle abc intersect at x,y,z. then prove that the measure of the angles of triangle abc are 90-1/2of a, 90-1/2 of b, 90-1/2 of c

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Grade:10

1 Answers

Arun
25757 Points
4 years ago
In ΔABC, by angle sum property we have 2x + 2y + ∠A = 180° ⇒ x + y + (∠A/2) = 90° ⇒ x + y = 90° –  (∠A/2)  à (1) In ΔBOC, we have  x + y + ∠BOC = 180° 90° – (∠A/2) + ∠BOC = 180° [From (1)] ∠BOC = 180° – 90° + (∠A/2)∠BOC = 90° + (∠A/2)

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