Question

9 if l || m and j || k, find the value of y.
a) 7
b) 13
c) 18
d) 65
e) 115

Explanation:

Step1: Set up supplementary angle equation

Since \( l \parallel m \), \( 5x \) and \( 7x+24 \) are same-side interior angles (supplementary):
$$5x + (7x + 24) = 180$$

Step2: Solve for x

Combine like terms and isolate x:
$$12x + 24 = 180$$
$$12x = 156$$
$$x = 13$$

Step3: Find angle measure on line l

Calculate \( 5x \):
$$5x = 5(13) = 65$$

Step4: Set up equal angle equation

Since \( j \parallel k \), \( 6y+7 \) and \( 5x \) are corresponding angles (equal):
$$6y + 7 = 65$$

Step5: Solve for y

Isolate y:
$$6y = 58$$
$$6y = 58$$
$$y = 13$$

Answer:

B) 13 spinning in circles