Question

geometry – unit 1 – parallel lines cut by a tran
solve each question as indicated. you must show a

1. what is the value of x in the figure below?

(figure shows two triangles with parallel bases, one with angle ((2x + 4)^circ) and the other with (38^circ))

Explanation:

Step1: Identify Alternate Interior Angles

The two triangles have parallel bases (indicated by the arrows), so the angles \((2x + 4)^\circ\) and \(38^\circ\) are alternate interior angles and thus equal. So we set up the equation:
\(2x + 4 = 38\)

Step2: Solve for \(x\)

Subtract 4 from both sides:
\(2x + 4 - 4 = 38 - 4\)
\(2x = 34\)

Divide both sides by 2:
\(\frac{2x}{2} = \frac{34}{2}\)
\(x = 17\)

Answer:

\(x = 17\)