Question

find the value of x that makes j || k
13.
14.
15.
16.
determine the missing angles.
17.
18.
19.
20.

Explanation:

Problem 13:

Step1: Identify angle relationship

Since \( j \parallel k \), the two angles \((3x + 10)^\circ\) and \((5x - 10)^\circ\) are alternate exterior angles, so they are equal.

$$ 3x + 10 = 5x - 10 $$

Step2: Solve for \( x \)

Subtract \( 3x \) from both sides:

$$ 10 = 2x - 10 $$

Add 10 to both sides:

$$ 20 = 2x $$

Divide by 2:

$$ x = 10 $$

Step1: Identify angle relationship

Since \( j \parallel k \), the angles \( 3x^\circ \) and \( 75^\circ \) are corresponding angles, so they are equal.

$$ 3x = 75 $$

Step2: Solve for \( x \)

Divide both sides by 3:

$$ x = 25 $$

Step1: Identify angle relationship

Since the two lines are parallel (vertical lines), the angles \( 6x^\circ \) and \((5x + 15)^\circ\) are corresponding angles, so they are equal.

$$ 6x = 5x + 15 $$

Step2: Solve for \( x \)

Subtract \( 5x \) from both sides:

$$ x = 15 $$

Answer:

\( x = 10 \)

Problem 14: