If angle 1 in the picture is , what is the measure of angle 3? Why?

(1 point)
63°63°
There is not enough information in the figure to establish this.
Angle 3 is 117° 117° because angle 1 and angle 3 form a line.
Angle 3 is 63°63° because angle 1 and angle 3 are corresponding angles.
Angle 3 is 63°63° because angle 1 and angle 3 are vertical angles.

1 answer

To determine the measure of angle 3 based on angle 1 being 63°, we consider the relationships between the angles provided in the options:

  1. Corresponding Angles: These would be equal if the lines are parallel and crossed by a transversal.
  2. Vertical Angles: These angles are always equal, formed when two lines intersect.
  3. Supplementary Angles: If angle 1 and angle 3 are on a straight line, they would add up to 180°.

Given the options, here's the analysis:

  • If angle 1 = 63°, and angle 3 is vertical to angle 1, then angle 3 = 63° (vertical angles).
  • If angle 1 and angle 3 form a straight line, then angle 3 = 180° - 63° = 117° (supplementary angles).
  • If angle 1 and angle 3 are corresponding angles (and assuming parallel lines), then angle 3 = 63°.

Without more context (for example, whether lines are parallel and the specific relationships between the angles), we cannot definitively conclude what angle 3 is from the information given.

However, if it is stated that angle 1 and angle 3 are on a straight line, then the correct answer would be that angle 3 is 117°, because the sum of angles on a straight line is 180°.

Conclusion: If angle 1 and angle 3 form a line, then angle 3 is 117° because they are supplementary angles.