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,<em> ∠1, ∠2 are supplementary by the defination of supplementary angles.</em>
 
        
                    
             
        
        
        
Answer:
x = 6
Step-by-step explanation:
Since KN is the perpendicular bisector, that means ∠KNM = ∠KNQ = 90° and MN = NQ so therefore, since they are right triangles, ΔKNM ≅ ΔKNQ because of HL. Therefore, KM = KQ by CPCTC so:
5x - 3 = 3x + 9
2x = 12
x = 6
 
        
             
        
        
        
Surface Area of Cube = width^2 * 6 (sides of the cube)
Therefore, (3.5)^2 * 6 = 
73.5 [whatever units]^2