Correct option :
[tex]\color{plum}\tt \: \bold{(A) 12x - 4 = 10x + 10 ; x = 7}[/tex]
Steps to derive the correct option :
Given :
- Lines u and v are parallel
- Measure of an angle = 12x - 4
- Measure of it's corresponding angle = 10x + 10
Since these angles are corresponding angles and lie on two parallel lines, their value will be equal.
Which means :
[tex] = \tt12x - 4 = 10x + 10[/tex]
[tex] = \tt12x - 4 - 10x = 10[/tex]
[tex] = \tt12x - 10x = 10 + 4[/tex]
[tex] = \tt2x = 14[/tex]
[tex] =\tt x = \frac{14}{2} [/tex]
[tex] =\color{plum}\tt x = 7[/tex]
Thus, the value of x = 7.
Let's place 7 in the place of x and see if their value matches :
[tex] = \tt12 \times 7 - 4[/tex]
[tex] = \tt84 - 4[/tex]
[tex] = \tt80[/tex]
Thus, ∠12x - 4 = 80°
[tex] =\tt 7 \times 10 + 7[/tex]
[tex] = \tt70 + 10[/tex]
[tex] = \tt80[/tex]
Thus, ∠10x + 10 = 80°
Since the value of these two angles are equal, we can conclude that we have found out the correct measure of each angle.
Therefore, the correct option is - (A) 12x - 4 = 10x + 10; x = 7
