Question

for #16-18, determine what type of angle pair is shown and find the value of x (and y).
16.
angle relationship: ____
x = ____
17.
angle relationship: ____
x = ____
18.
angle relationship: ____
x = ____
y = ____

Explanation:

Problem 16

Step1: Identify angle relationship

The angles \(60^\circ\) and \((4x - 12)^\circ\) are corresponding angles (since the lines are parallel and cut by a transversal), so they are equal.

Step2: Set up equation and solve

\(4x - 12 = 60\)
Add 12 to both sides: \(4x = 60 + 12 = 72\)
Divide by 4: \(x = \frac{72}{4} = 18\)

Step1: Identify angle relationship

The angles \((11x - 28)^\circ\) and \((7x - 8)^\circ\) are alternate interior angles (since lines are parallel and cut by a transversal), so they are equal.

Step2: Set up equation and solve

\(11x - 28 = 7x - 8\)
Subtract \(7x\) from both sides: \(4x - 28 = -8\)
Add 28 to both sides: \(4x = -8 + 28 = 20\)
Divide by 4: \(x = \frac{20}{4} = 5\)

Step1: Identify angle relationships

• \(75^\circ\) and \((4x + 9)^\circ\): Corresponding angles (equal).
• \(75^\circ\) and \((3y)^\circ\): Supplementary angles (sum to \(180^\circ\)) or \( (4x + 9)^\circ\) and \((3y)^\circ\) are supplementary (linear pair).

Step2: Solve for \(x\)

\(4x + 9 = 75\)
Subtract 9: \(4x = 75 - 9 = 66\)
Divide by 4: \(x = \frac{66}{4} = 16.5\)

Step3: Solve for \(y\)

\(3y + 75 = 180\) (supplementary)
Subtract 75: \(3y = 180 - 75 = 105\)
Divide by 3: \(y = \frac{105}{3} = 35\)

Answer:

Angle Relationship: Corresponding Angles
\(x = 18\)

Problem 17