Vertical Angle Relationships

Question

12345

Answer

∠A and ∠B are vertical angles with  m∠A = x and m∠B= 5x-80
  ∠C and ∠D are vertical angles with  m∠C = -3x+58 and m∠D= x-2
  ∠E and ∠F are vertical angles with  m∠E= 5x+10 and m∠F= 7x-12
  Due to vertical angles :
  m∠PTS = m∠RTQ ..............................Vertical angles
  
m∠A = m∠B...........................measure of vertical angles are equal
  
x = 5x-80,   
or 5x - x = 80,
  
or 4x = 80,   
or x = 20
  
m∠A = x = 20
  
 
  
m∠A = m∠B...........................measure of vertical angles are equal
  
-3x+58 = x-2,
  
 or x + 3x = 58+2 ,   
or 4x = 60,   
or x = 15
  
m∠D = x-2  = 15-2 = 13
  
 
  
m∠E = m∠F...........................measure of vertical angles are equal
  
5x+10 = 7x-12,       or 7x - 5x = 10+12 ,   
or 2x = 22,                 or x = 11
  
 
  
5(x - 4) = 4x + 7   
5x – 20 = 4x + 7   
5x -4x = 7 + 20
  
x = 27o 
  
 
  
11(y-10) =  4y – 5
  
11y – 110 = 4y – 5
  
11y – 4y = -5 + 110
  
7y = 105   or  y = 105/7 = 15o
  
m∠PTS = 11(y-10) = 11(15 -10) = 55o

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Vertical Angle Relationships

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