In the given figure, the bisectors if angle ABC and angle BCA , intersect each other at point O. If angle BOC=100 , then find A need step by step explanation
Answers
Answer:
20
Step-by-step explanation:
Bisectors of angle ABC and angle BCA , intersect each other at point O .
∠BOC = 100°
To find:
Measure of ∠A.
Solution:
Let the measure of ∠OBC be x and ∠OCB be y.
In triangle OBC, using angle sum property, we get
\angle OBC+\angle OCB+\angle BOC=180^{\circ}∠OBC+∠OCB+∠BOC=180
∘
x+y+100^{\circ}=180^{\circ}x+y+100
∘
=180
∘
x+y=180^{\circ}-100^{\circ}x+y=180
∘
−100
∘
x+y=80^{\circ}x+y=80
∘
...(i)
Bisectors of angle ABC and angle BCA , intersect each other at point O .
So, ∠ABC is 2x and ∠ACB be 2y.
In triangle ABC, using angle sum property, we get
\angle ABC+\angle ACB+\angle BAC=180∠ABC+∠ACB+∠BAC=180
2x+2y+\angle A=180^{\circ}2x+2y+∠A=180
∘
2(x+y)+\angle A=180^{\circ}2(x+y)+∠A=180
∘
2(80^{\circ})+\angle A=180^{\circ}2(80
∘
)+∠A=180
∘
[Using (i)]
160^{\circ}+\angle A=180^{\circ}160
∘
+∠A=180
∘
\angle A=180^{\circ}-160^{\circ}∠A=180
∘
−160
∘
\angle A=20^{\circ}∠A=20