Given:
Vertical angles.
One angle is 85°.
To find:
The measure of ∠1, ∠2 and ∠3.
Solution:
∠2 and 85° are vertically opposite angles and ∠1 and ∠3 are vertically opposite angles.
Vertical angle theorem:
If two lines are intersecting, then the vertically opposite angles are congruent.
⇒ m∠2 = 85°
Sum of the adjacent angles in a straight line = 180°
m∠2 + m∠3 = 180°
85° + m∠3 = 180°
Subtract 85° from both sides.
85° + m∠3 - 85° = 180° - 85°
m∠3 = 95°
By vertical angle theorem:
⇒ m∠1 = m∠3
⇒ m∠1 = 95°
Therefore m∠1 = 95°, m∠2 = 85° and m∠3 = 95°.
 
        
             
        
        
        
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The solution for the given equations  x + 3y = 5 and x - 3y = -1 are x=2 and y=1.
Step-by-step explanation:
The given is,
             ......................................(1)
......................................(1)
             ....................................(2)
....................................(2)
Step:1
          By elimination method,
          Subtracting Equations (1) and (2),
                      
                      
              ( - )
            (  ) + (
 ) + (  ) = (
 ) = (  )
 )
                                         = 6
 = 6
                                           = 1
 = 1
Step:2
         Substitute the value of y in equation (1),
                              
                         + ( 3 × 1 ) = 5
 + ( 3 × 1 ) = 5
                                        = 5-3
 = 5-3
                                        = 2
 = 2
Step:3
         Check for Solution,
         Substitute the values of x and y in Eqn (1),
                                   
                            2 + ( 3 × 1 ) = 5
                                           5 = 5
Result:
        The solution for the given equations  x + 3y = 5 and x - 3y = -1 are x=2 and y=1, by elimination method.
 
        
             
        
        
        
Answer:
6 
Step-by-step explanation:
2 books in each box. 
There are three boxes
2 times 3 equals 6