Question

1. decide what kind of angles are pictured above.

alternate exterior angles alternate interior angles same - side interior angles corresponding angles

1. decide whether the angles are congruent or supplementary. drag the values from the diagram into the correct equation and solve for x.
2. solve for x, then any requested angles.

x = m∠1 = °

Explanation:

Step1: Determine the relationship between the angles

Since the angles \(5x\) and \(130^{\circ}\) are alternate exterior angles, and for parallel lines cut by a transversal, alternate exterior angles are congruent. So the equation is \(5x=130\).

Step2: Solve for \(x\)

Divide both sides of the equation \(5x = 130\) by \(5\).

$$x=\frac{130}{5}=26$$

Step3: Find \(m\angle1\)

\(\angle1\) and \(5x\) are supplementary (they form a linear - pair). Since \(x = 26\), then \(5x=5\times26 = 130\).
Using the linear - pair relationship \(m\angle1+5x=180^{\circ}\), substitute \(5x = 130^{\circ}\) into the equation.

$$m\angle1=180 - 130=50^{\circ}$$

Answer:

\(x = 26\), \(m\angle1=50\)