Measure of ∠6 = (3x + 7)°
Measure of ∠7 = 76°
∠6 and ∠7 are vertically opposite angles, so their measures will be equal.
Which means :
[tex] = 3x + 7 = 76[/tex]
[tex] = 3x = 76 - 7[/tex]
[tex] = 3x = 69[/tex]
[tex] = x = \frac{69}{3} [/tex]
[tex]\color{hotpink} = x = 23[/tex]
Let us now place 23 in the place of x and see if it forms 76 :
[tex] = 3x + 7 = 76[/tex]
[tex] = 3 \times 23 + 7 = 76[/tex]
[tex] = 69 + 7 = 76[/tex]
[tex] = 76 = 76[/tex]
Thus, the value of x we found is correct.
Therefore, the value of x = 23
