It is given that m || n , m∠1 = 65° , m∠2 = 60° , and BD bisects ∠ABC .
Because of the triangle sum theorem, m∠3 = 55°.
By the definition of bisector, m∠ABC = 110°. (unsure of this one, but no other choice seems right)
m∠5 = 110° because vertical angles are congruent.
Because of the same-side interior angles theorem, m∠5 + m∠6 = 180°.
Substituting gives 110° + m∠6 = 180° .
So, by the subtraction property of equality, m∠6 = 70°