Answer:
The rest of question m∠2 = 60°
The prove is as following:
It is given that m∥n , m∠1=65° , m∠2=60° , and BD bisects ∠ABC .
Because of the triangle sum theorem, m∠3= 180° - (65°+60°) = 55° .
∠3 =∠4 By the (Angle Bisector Theorem) ⇒ m∠4=55° .
Using the (Sum of Adjacent Angles), m∠ABC = ∠3 +∠4= 110° .
m∠5 = m∠ABC = 110° because vertical angles are congruent.
m∠5 + m∠6 = 180° ⇒ Co-interior angle property
Substituting gives 110° + m∠6 = 180°
So, m∠6 = 180° - 110° = 70°
