Question

Lines AB and CD are parallel. If 7 measures (3x + 7)°, and 6 measures 76°, what is the value of x?

Answer 1

Measure of ∠6 = (3x + 7)°

Measure of ∠7 = 76°

∠6 and ∠7 are vertically opposite angles, so their measures will be equal.

Which means :

`= 3x + 7 = 76`

`= 3x = 76 - 7`

`= 3x = 69`

`= x = (69)/(3)`

`\color{hotpink} = x = 23`

Let us now place 23 in the place of x and see if it forms 76 :

`= 3x + 7 = 76`

`= 3 * 23 + 7 = 76`

`= 69 + 7 = 76`

`= 76 = 76`

Thus, the value of x we found is correct.

Therefore, the value of x = 23