Question

Two intersecting lines create four angles triangle one and triangle three are a vertical pair. There’s some of of their measures is equal to 68° what equation solves for the value of each angle.
2X +68 equals 180°
6X degrees equals 2°
2X degrees equals 68°
X degree equals 68°

Answer 1

To solve the problem, let's first understand what is provided. We have two intersecting lines that form four angles, and we know that angles one and three are a vertical pair. This means they are equal in measure.

If the sum of the measures of angles one and three is equal to 68°, then we can express this relationship mathematically.

Using the information given, we have two angles (let’s denote them as Angle 1 and Angle 3) such that:

\[ \text{Angle 1} + \text{Angle 3} = 68° \]

Since they are a vertical pair, we can say:

\[ \text{Angle 1} = \text{Angle 3} \]

Let’s denote the measure of each angle as \( x \). This leads us to the equation:

\[ x + x = 68° \]
\[ 2x = 68° \]

Now we can solve for \( x \):

\[ x = \frac{68°}{2} \]
\[ x = 34° \]

Therefore, each angle measures 34°.

Regarding the options provided, only one option mirrors this process. Let’s evaluate them:

1. **2X + 68 = 180°** - This does not apply since it sums to 180°.
2. **6X = 2** - This does not relate to our angles.
3. **2X = 68°** - This is correct as derived above.
4. **X = 68°** - This is incorrect since \( x \) has been calculated as 34°.

Thus, the equation that correctly solves for the value of each angle is:

**2X = 68°**.