Use the figure to answer the question.

Question

Two intersecting lines form an x and have four angles at the point of intersection labeled clockwise from the top: 1, 2, 3, and 4.

If angle 1 in the picture is 63° , what is the measure of angle 3? Why?

(1 point)
Responses

Angle 3 is 117° because angle 1 and angle 3 form a line.
Angle 3 is 117 degrees because angle 1 and angle 3 form a line.

Angle 3 is 63° because angle 1 and angle 3 are corresponding angles.
Angle 3 is 63 degrees because angle 1 and angle 3 are corresponding angles.

Angle 3 is 63° because angle 1 and angle 3 are vertical angles.
Angle 3 is 63 degrees because angle 1 and angle 3 are vertical angles.

There is not enough information in the figure to establish this.
There is not enough information in the figure to establish this.
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Answer 1

To determine the measure of angle 3 given that angle 1 is 63°, we can analyze the relationship between the angles created by the intersection of the two lines.

Angle 1 and angle 3 are opposite each other at the point of intersection. Angles that are opposite each other when two lines intersect are called vertical angles. Vertical angles are always equal in measure.

Since angle 1 is 63°, angle 3 must also be 63° because they are vertical angles.

Therefore, the correct response is: Angle 3 is 63° because angle 1 and angle 3 are vertical angles.