In the given figure triangle ABC is an isosceles triangle in which AB=AC and angle A=50° , find the measure of angle B and angle C
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Answered by
1
Since,
AB=AC..........(1)
OB is the bisector of ∠B
So, ∠ABO=∠OBC=
2
1
∠B.......(2)
OC is the bisector of ∠C
So, ∠ACO=∠OCB=
2
1
∠C.......(3)
⇒∠ACB=∠ABC (Angles opposite to equal sides are equal)
2
1
∠ACB=
2
1
∠ABC
∠OCB=∠OBC From (2) and (3)
Hence,
OB=OC (Sides opposite to equal angles are equal)
Hence proved.
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Answered by
15
Answer:
∠B = ∠C = 65°
Step-by-step explanation:
The tringle given in the figure is an isosceles triangle.
An important property of isosceles triangles is that, since two given sides are equal, the corresponding angles opposite to those sides will be equal.
∴ Since AB = AC, ∠B = ∠C
Since ∠B = ∠C, let ∠B = ∠C = x
∴ ∠A + ∠B + ∠C = 180° ---------- Angle sum property of triangles.
∴ 50° + x + x = 180°
2x = 130°
∴ x = 65°
∴ ∠B = ∠C = x = 65°
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