Given: m∥n , m∠1=65∘ , m∠2=60∘ , and bd−→− bisects ∠abc . prove: m∠6=70∘

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 ∠3≅∠4 , so m∠4=55∘ . using the m∠abc=110∘ . m∠5=110∘ because vertical angles are congruent. because of the m∠5+m∠6=180∘ . substituting gives 110∘+m∠6=180∘ . so, by the m∠6=70∘ .