Respuesta :
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:
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.
