Question

atg 2) use your knowledge of parallel lines and angle relationships to write an equation that can be used to solve for. state the theorem that you used to determine the relationship between the given angles.
what theorem can be used to determine the relationship between the given angles?
a corresponding angles theorem
b alternate interior angles theorem
c alternate exterior angles theorem
d same side interior angles theorem
e same side exterior angles theorem
f linear pair postulate
g vertical angles theorem
write an equation and solve for x. x =

Explanation:

Step1: Identify the theorem

The angles \((16x + 22)^{\circ}\) and \(134^{\circ}\) are same - side exterior angles. When two parallel lines \(l\) and \(m\) are cut by a transversal, the same - side exterior angles are supplementary. So we use the Same Side Exterior Angles Theorem.

Step2: Write the equation

Since the angles are supplementary, we have the equation \((16x + 22)+134 = 180\).
Simplify the left - hand side: \(16x+22 + 134=16x + 156\). So the equation becomes \(16x+156 = 180\).

Step3: Solve for \(x\)

Subtract \(156\) from both sides of the equation: \(16x+156-156 = 180 - 156\).
We get \(16x=24\).
Divide both sides by \(16\): \(x=\frac{24}{16}=\frac{3}{2}=1.5\).

Answer:

The theorem is the Same Side Exterior Angles Theorem. The value of \(x\) is \(1.5\).