Question

Two intersecting lines create four angles; < 1 and < 3 are a vertical pair. The sum of their measures is equal to 68. Which two equations would solve for the value of each angle? A: 2x + 68 = 180 B: x + x = 68 C: 2x = 68 D: x = 68

Answer 1

To solve for the measures of angles <1 and <3, which are vertical angles, we know that vertical angles are equal. Therefore, if we let the measure of angle <1 be \( x \), then the measure of angle <3 is also \( x \).

Since the problem states that the sum of their measures is equal to 68, we can write the equation:

\[
x + x = 68
\]

This simplifies to:

\[
2x = 68
\]

From here, we can find the value of \( x \) by solving for it:

1. Divide both sides by 2:
\[
x = 34
\]

Now, let's identify which equations from your list are necessary to solve for the value of each angle:

- Option A: \( 2x + 68 = 180 \) (Not needed)
- Option B: \( x + x = 68 \) (Needed)
- Option C: \( 2x = 68 \) (Needed)
- Option D: \( x = 68 \) (Not needed)

The two equations that would solve for the value of each angle are:

**B: \( x + x = 68 \)** and **C: \( 2x = 68 \)**.