Question

Two intersecting lines create four angles; ∠1 and ∠3 are a vertical pair. Their sum of their measures is equal to 68° . What equation solves for the value of each angle?(1 point)Responses

Answer 1

[AI-generated answer — Bot GPT-4o]

To solve for the value of each angle when two intersecting lines create four angles and ∠1 and ∠3 are a vertical pair, we need to understand the properties of vertical angles. Vertical angles are always equal to each other.

Given that the sum of their measures is 68°, we can set up the following equation:

Since ∠1 = ∠3 and their sum is 68°:
\[ ∠1 + ∠3 = 68° \]

But because ∠1 and ∠3 are equal:
\[ ∠1 + ∠1 = 68° \]

This simplifies to:
\[ 2∠1 = 68° \]

To solve for ∠1, we divide both sides by 2:
\[ ∠1 = \frac{68°}{2} \]
\[ ∠1 = 34° \]

Since ∠1 = ∠3:
\[ ∠3 = 34° \]

Therefore, the value of each angle is 34°. The equation that solves for the value of each angle is:
\[ 2∠1 = 68° \]