Question

in an isoscels triangle abc the bisectors of angle b and angle c meets at apoint o.if angle a =40° then angle boc =?

Answer 1

It's an isoceles triangle. so the base angles are equal. using angle sum property of triangle ABC

Let us take angleABC as x.
angleABC=angleACB(isoceles triangle)

angleABC+angleACB+angleBAC=180°
40°+x°+x°=180°
2x°=180-40
x=140/2
angle x=70°

angles B and C are bisected and produced to O

angleBOC=180°-angleOBC-angleOCB(angle sum property of triangle BOC)
angleBOC=180°-2(70/2){angular bisectors}
angleBOC=180-70
angleBOC=110°