Question

given ( l parallel m parallel n ), find the value of ( x ).
(there is a diagram with three parallel lines ( l ), ( m ), ( n ) and a transversal creating an angle of ( (6x - 2)^circ ) between ( l ) and ( m ), and an angle of ( 52^circ ) between ( n ) and the transversal. below is an answer section with ( x = ) input box and a submit answer button, and text attempt 1 out of 2.)

Explanation:

Step1: Identify supplementary angle

The angle supplementary to $52^\circ$ is $180^\circ - 52^\circ = 128^\circ$.

Step2: Set equal to given angle

Since $l \parallel m \parallel n$, $(6x-2)^\circ$ equals $128^\circ$:
$$6x - 2 = 128$$

Step3: Solve for x

Add 2 to both sides:
$$6x = 128 + 2 = 130$$
Divide by 6:
$$x = \frac{130}{6} = \frac{65}{3} \approx 21.67$$

Answer:

$x = \frac{65}{3}$ or $x \approx 21.67$