Can anyone please help me with this? You need to find the equation to solve for x, the value of x, and the value of each angle measure for all 5 questions. I will give brainliest

1. a) 3x + 21 = 6x - 60

  b) x = 27

  c) angle measure = 102º

2. a) 12x - 18 = 8x + 10

   b) x = 7

   c) angle measure = 66º

3. a) 7x + 9 + 5x + 3 = 180 (simplified: 12x + 12 = 180)

   b) x = 14

   c) 107º; 73º

4. a) 3x + 10 + 3x -28 = 180 (simplified: 6x -18 = 180)

   b) x = 33

   c) 109º; 71º

5. a) 12x + 15 = 15x

   b) x = 5

   c) 75º

Step-by-step explanation:

1. a) they're the same angle so set them equal to each other: 3x + 21 = 6x - 60

  b) solve from the equation above

      3x + 21 = 6x - 60        subtract 3x from both sides

       21 = 3x - 60                add 60 to both sides

       81 = 3x                        divide both sides by 3

       x = 27

  c) plug back into each equation (they should be the same, but do both just to check)

      3(27) + 21 = 81 +21 = 102º

      6(27) - 60 = 162 - 60 = 102º

2. a) again, they're the same angle measure so set them equal to each other: 12x - 18 = 8x + 10

   b) solve the equation for x

      12x - 18 = 8x + 10            subtract 8x from both sides

       4x - 18 = 10                     add 18 from both sides

       4x = 28                           divide both sides by 4

       x = 7

  c) plug back into each equation (they should be the same, but do both just to check)

      12(7) - 18 = 84 - 18 = 66º

      8(7) + 10 = 56 + 10 = 66º

3.  a) the sum of the two angles is 180º so 7x + 9 + 5x + 3 = 180

         if you want the equation simplified: 12x +12 = 180

     b) solve for x, i will be using the simplified equation

         12x + 12 = 180            subtract 12 from both sides

         12x = 168                    divide both sides by 12

         x = 14            

     c) plug into each equation to get the two angle measures

         7(14) + 9 = 98 + 9 = 107º

         5(14) + 3 = 70 + 3 = 73º

4. a) the sum of the two angles is 180º so 3x + 10 + 3x -28 = 180

       if you want it simplified: 6x -18 = 180

   b) solve for x, i will be using the simplified equation

       6x - 18 = 180                    add 18 to both sides

       6x = 198                           divide both sides by 6

       x = 33

   c) plug into each equation to get the two angle measures

      3(33) + 10 = 99 + 10 = 109º

      3(33) - 28 = 99 - 28 = 71º

5. a) they're the same angle measure so set them equal to each other: 12x + 15 = 15x

   b) solve for x with the equation above

        12x + 15 = 15x                   subtract 12x from both sides

        15 = 3x                              divide both sides by 3

        x = 5

  c) plug back into each equation (they should be the same, but do both just to check)

      12(5) + 15 = 60 + 15 = 75º

      15(5) = 75º    

the expected value of the random variable : 0, 1 and 2

step-by-step explanation: