Question

HELP PLEASE !!!

Answer 1

Given: m ∠3 = m ∠4

To Prove: ∠1, ∠2 are supplementary .

Proof : m ∠3 = m ∠4    ( Given)                                              ------------(1)

m<2 + m< 3 = 180 degrees  ( <2 and <3 form a linear pair). ----------(2)

m< 4 = m<1                            (Vertical angles are equal)       -----------(3).

Substituting, m<4 =m<1 in (1), we get

m ∠3 = m ∠1.

Now, substituting m ∠3 = m ∠1 in (2), we get

m<2 + m< 1 = 180 degrees.

Sum of m <1 and m<2 is 180 degrees.

Therefore, ∠1, ∠2 are supplementary by the defination of supplementary angles.

Answer 2

Answer:

The required proof is shown below.

Step-by-step explanation:

Consider the provided information.

Two Angles are Supplementary when they add up to 180 degrees.

Substitution property: if x = y, then x can be replace by y in any equation, and y can be replaced by x in any equation.

Opposite angles are vertical angles and they are always congruent,

Statement                                    Reason

1)  m∠3=m∠4                               Given

2) ∠2, ∠3 are supplementary    Their 2 non-common sides in 1 ray

3) m∠2+m∠3=180°                      Definition of supplemental angles

4) m∠2+m∠4=180°                      Substitution

5) m∠1=m∠4                               Opposite angles are congruent

6) m∠2+m∠1=180°                      Substitution

7) ∠1, ∠2                                      Definition of supplementary angles

Hence, the required proof is shown above.