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 x°=68° x equals 68 degrees 2x°+68°=180° 2 x plus 68 degrees equals 180 degrees 68x°=2° 68 x equals 2 2x°=68°
Answers
GPT 3.5
The correct equation to solve for the value of each angle is:
2x° + 68° = 180°
Here's why:
- ∠1 and ∠3 are a vertical pair, which means they are congruent (have the same measure).
- The sum of the measures of all four angles formed by the intersecting lines is 360° (since they form a straight line).
- The sum of ∠1 and ∠3 is equal to the sum of the other two angles (∠2 and ∠4).
- If we let x° be the measure of ∠1 (and ∠3), then ∠2 (and ∠4) would have a measure of x° as well.
- So, the equation becomes: x° + x° + 68° = 360°
- Simplifying, we get: 2x° + 68° = 360°
- From this equation, we can solve for x° to find the value of each angle.
2x° + 68° = 180°
Here's why:
- ∠1 and ∠3 are a vertical pair, which means they are congruent (have the same measure).
- The sum of the measures of all four angles formed by the intersecting lines is 360° (since they form a straight line).
- The sum of ∠1 and ∠3 is equal to the sum of the other two angles (∠2 and ∠4).
- If we let x° be the measure of ∠1 (and ∠3), then ∠2 (and ∠4) would have a measure of x° as well.
- So, the equation becomes: x° + x° + 68° = 360°
- Simplifying, we get: 2x° + 68° = 360°
- From this equation, we can solve for x° to find the value of each angle.