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

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

The correct response is:

Angle 3 is 117° because angle 1 and angle 3 form a straight line. When two lines intersect, they form two pairs of vertical angles, and each pair of vertical angles are congruent. Therefore, angle 1 and angle 3 are vertical angles, and since the sum of angles on a straight line is 180°, angle 3 must be 117°.

To determine the measure of angle 3, we need to analyze the given figure.

First, let's understand what corresponding angles and vertical angles mean:

1. Corresponding angles: When two lines are crossed by a transversal, the angles on the same side of the transversal and in the same position are called corresponding angles.

2. Vertical angles: When two lines intersect, the opposite angles formed at the point of intersection are called vertical angles.

From the provided options, we can eliminate the response "Angle 3 is 117° because angle 1 and angle 3 form a line" because angles 1 and 3 do not form a straight line. Therefore, the correct answer is either "Angle 3 is 63° because angle 1 and angle 3 are corresponding angles" or "Angle 3 is 63° because angle 1 and angle 3 are vertical angles."

Now, let's determine which of these two answers is correct. Since the information mentioned is a) angle 1 is 63° and b) angle 1 and angle 3 are corresponding angles, we can conclude that angle 3 is indeed 63°. Therefore, "Angle 3 is 63° because angle 1 and angle 3 are corresponding angles" is the correct answer.

1. Corresponding Angles

2. Alternate Exterior Angles
3. Angle 3 is 63 degrees because angles 1 and 3 are vertical angles
4. The supplement is 95 degrees because 180 degrees - 85 degrees = 95
5. ∠1,∠5, and ∠8 are congruent to ∠4