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?
There is not enough information in the figure to establish this.
Angle 3 is 63° because angle 1 and angle 3 are vertical angles.
Angle 3 is 117° because angle 1 and angle 3 form a line.
Angle 3 is 63° because angle 1 and angle 3 are corresponding angles.
wrong. Angles 1 and 3 are vertical angles.
So, A
pologies for the mistake, you are correct.
Angle 3 is 63° because angle 1 and angle 3 are vertical angles. Vertical angles are formed when two lines intersect and are opposite each other. They have equal measures, so if angle 1 is 63°, then angle 3 must also be 63°.
Angle 3 is 117° because angle 1 and angle 3 are vertical angles. Vertical angles are formed by two intersecting lines and are congruent to each other. Since angle 1 is 63°, angle 3 must also be 63° in order to be congruent to angle 1.
To determine the measure of angle 3, we need to examine the relationship between angle 1 and angle 3. Based on the information provided, we can consider a few possibilities:
1. If angle 1 and angle 3 are vertical angles, then they have equal measures. Vertical angles are formed when two lines intersect, and they share a common vertex but not any sides. In this case, the measure of angle 3 would also be 63°.
2. If angle 1 and angle 3 form a straight line or a straight angle, then they add up to 180°. A straight angle is formed when two lines are in a straight line, and they have a common vertex at the point of intersection. In this case, if angle 1 is 63°, angle 3 would be 180° - 63° = 117°.
3. If angle 1 and angle 3 are corresponding angles, then they have equal measures. Corresponding angles are formed when a transversal intersects two parallel lines, and they are located at the same corresponding positions on each of the lines. However, based on the given figure, it is not explicitly mentioned or shown that the lines are parallel and intersected by a transversal. Without confirmation, we cannot assume they are corresponding angles.
In conclusion, given the lack of additional information or details about the specific characteristics of the lines in the figure, we cannot determine the measure of angle 3 with certainty.
The correct answer is:
Angle 3 is 117° because angle 1 and angle 3 form a line. When two lines intersect, the sum of the angles on one side of the intersection is always 180°. Since angle 1 is 63°, angle 3 can be found by subtracting angle 1 from 180°: 180° - 63° = 117°.