Question

Drag and drop an answer to each box to correctly complete the proof

Given: m || n, m angle 1 = 65° and BD bisects angle ABC
Prove: m/6 = 70°​

Answer 1

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°