Question

1. name the type of angles shown. write and solve an equation to find the value of x.

$96^circ$ $(6x)^circ$ $x = $

$(3x + 1)^circ$ $85^circ$ $x = $

Explanation:

Left Diagram:

Step1: Identify angle type (Alternate Interior Angles)

The angles \(96^\circ\) and \((6x)^\circ\) are Alternate Interior Angles (since lines are parallel, alternate interior angles are equal). So, \(6x = 96\).

Step2: Solve for \(x\)

Divide both sides by 6: \(x=\frac{96}{6}=16\).

Step1: Identify angle type (Corresponding Angles)

The angle \((3x + 1)^\circ\) and \(85^\circ\) are Corresponding Angles (since lines are parallel, corresponding angles are equal). So, \(3x + 1 = 85\).

Step2: Solve for \(x\)

Subtract 1: \(3x = 85 - 1 = 84\).
Divide by 3: \(x=\frac{84}{3}=28\).

Answer:

\(x = 16\)

Right Diagram: