Question

1. find x that would make u || v

the given angles are angles.
the equation to find x would be:
x=

Explanation:

Step1: Identify the type of angles

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary (sum to \(180^{\circ}\)). The given angles \(60^{\circ}\) and \(x + 129\) are consecutive interior angles.

Step2: Set up the equation

Since consecutive interior angles are supplementary when \(u\parallel v\), we have the equation \(60+(x + 129)=180\).

Step3: Solve the equation for \(x\)

First, simplify the left - hand side of the equation: \(x+189 = 180\).
Then, subtract \(189\) from both sides: \(x=180 - 189\).
So, \(x=-9\).

Answer:

The given angles are consecutive interior angles. The equation to find \(x\) would be \(60+(x + 129)=180\). \(x = - 9\)