If the vertical angle of a triangle is 130 degrees then the angle between the bisecting of the base angles - Maths - Lines and Angles

Question

If the vertical angle of a triangle is 130 degrees then the angle
between the bisecting of the base angles of the triangle is?

Ashwini Kumar · Accepted Answer

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We have,ABC is a triangle in which ∠BAC=130°Now,∠ABC+∠BCA+∠BAC=180°⇒∠ABC+∠BCA+130°=180°⇒∠ABC+∠BCA=50°      
1Now,∠OBC+∠OCB+∠BOC=180°⇒∠OBC+∠OCB=180°-∠BOC⇒2∠OBC+∠OCB=2180°-∠BOC⇒2∠OBC+2∠OCB=2180°-∠BOC⇒∠ABC+∠BCA=360°-2∠BOC                        ∵OB and OC are bisector of ∠ABC and ∠BCA respectively⇒50°=360°-2∠BOC      From 1⇒2∠BOC=360°-50°⇒2∠BOC=310°∴∠BOC=155°

If the vertical angle of a triangle is 130 degrees then the angle between the bisecting of the base angles of the triangle is?