If m<ABC=x and m<BAC=m<BCA=2x-10, is line BF an altitude? Explain.

Question

m<ABC=x

m<BAC= m<BCA=2x-10

Answer 1

Two angles have the same measure (2x-10) so the triangle is isosceles.

The sum of the angles is x+2(2x-10)=x+4x-20=5x-20=180, 5x=200, x=40°.

The angles are 40°, 70° and 70°. There's no picture so BF is a perpendicular bisector of AC, which is also the altitude, if BF bisects AB̂C. This is a property of isosceles triangles. mAB̂F=mCB̂F=20°.