In ΔABC, the bisectors of ∠ABC and ∠BCA intersect each other at O. The measure of ∠BOC is
(a) 90° + ∠A
(b) 90° + ∠A2
(c) 180 – ∠A
(d) 90° – ∠A2
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Answers
Given : In ΔABC, the bisectors of ∠ABC and ∠BCA intersect each other at O.
To Find : The measure of ∠BOC is
(a) 90° + ∠A
(b) 90° + ∠A/2
(c) 180 – ∠A
(d) 90° – ∠A/2
Solution:
Sum of angles of a triangle is 180°.
Angle bisector divided angle in two equal half
In ΔABC
∠A + ∠B + ∠C = 180°
=> ∠B + ∠C = 180° - ∠A Eq1
bisectors of ∠ABC and ∠BCA intersect each other at O.
=> ∠OBC = (1/2) ∠B and ∠OCB = (1/2)∠C
in ΔOBC
∠OBC + ∠OCB + ∠BOC = 180°
=> (1/2) ∠B + (1/2)∠C + ∠BOC = 180°
=> (1/2) ( ∠B + ∠C) + ∠BOC = 180°
From Eq1 ∠B + ∠C = 180° - ∠A
=> (1/2) ( 180° - ∠A) + ∠BOC = 180°
=> 90° - ∠A/2 + ∠BOC = 180°
=> ∠BOC = 180° - 90° + ∠A/2
=> ∠BOC = 90° + ∠A/2
The measure of ∠BOC is 90° + ∠A/2
Correct option is option b) 90° + ∠A/2
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Answer:
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