Question

GEOMETRY HELP PLEASE!!!!!!! I REALLY NEED HELP FAST!!!!!!! I WILL GIVE BRAINLIEST!

Answer 1

Answer:

2.  Definition of linear pair; 3.  Angles in a linear pair are supplementary; 4.  Definition of supplementary; 5.  m∠1+m∠2+m∠3 = 180°; 6.  Substitution; 7.  m∠1+m∠2 = m∠4, substitution property of equality

Step-by-step explanation:

A linear pair is two angles that together form a straight line.  ∠3 and ∠4 together form a straight line, so they are a linear pair.

The angles in a linear pair are supplementary.  This means that ∠3 and ∠4 are supplementary.  

Supplementary angles sum to 180°; this means that m∠3+m∠4 = 180°.

The Triangle Sum Theorem states that the three angles of a triangle have measures that sum to 180°.  This means that m∠1+m∠2+m∠3 = 180°.

Substituting m∠3+m∠4 for 180° gives us m∠1+m∠2+m∠3 = m∠3+m∠4.

Subtracting m∠3 from each side, using the substitution property of equality, gives us

m∠1+m∠2 = m∠4.

Answer 2

2. Definition of linear pair

3. Linear pair theorem

4. Definition of supplementary angles

5. m<1 + m<2 + m<3 = 180

6. Substitution property of equality

7. m<1 + m<2 + m<4

7. Subtraction property of equality