Question

Lines m and n are parallel. ∠A=(4x−13)° and ∠G=(2x+43)° . What is the value of x ? (1 point)
28
50
25
56

Answer 1

Since lines \( m \) and \( n \) are parallel, the angles \( \angle A \) and \( \angle G \) must be corresponding angles. Therefore, we can set up the equation:

\[
4x - 13 = 2x + 43
\]

Now, let's solve for \( x \):

1. Subtract \( 2x \) from both sides:

\[
4x - 2x - 13 = 43
\]

This simplifies to:

\[
2x - 13 = 43
\]

2. Next, add 13 to both sides:

\[
2x = 43 + 13
\]

This simplifies to:

\[
2x = 56
\]

3. Now, divide both sides by 2:

\[
x = \frac{56}{2} = 28
\]

Thus, the value of \( x \) is \( 28 \).