Question

Consider that lines u and vare parallel. Which equation models the relationship between the angles? What is the value of x?

Answer 1

Correct option :

$\color{plum}\tt \: \bold{(A) 12x - 4 = 10x + 10 ; x = 7}$

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 :

$= \tt12x - 4 = 10x + 10$

$= \tt12x - 4 - 10x = 10$

$= \tt12x - 10x = 10 + 4$

$= \tt2x = 14$

$=\tt x = \frac{14}{2}$

$=\color{plum}\tt x = 7$

Thus, the value of x = 7.

Let's place 7 in the place of x and see if their value matches :

• 12x - 4

$= \tt12 \times 7 - 4$

$= \tt84 - 4$

$= \tt80$

Thus, ∠12x - 4 = 80°

• 10x + 10

$=\tt 7 \times 10 + 7$

$= \tt70 + 10$

$= \tt80$

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