Question

Lines m and n are parallel, ∠A = (4x-13) degree and ∠G = (2x + 43) degree. What is the value of x?

a. 25
b. 56
c. 50
d. 28

Answer 1

Since lines \( m \) and \( n \) are parallel, the angles \( \angle A \) and \( \angle G \) must be equal because they are corresponding angles.

So, we set up the equation:

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

Now, we'll solve for \( x \).

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

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

2. Add 13 to both sides:

\[
2x = 43 + 13
\]
\[
2x = 56
\]

3. Divide both sides by 2:

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

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