If angle 1 in the picture is 63 degrees, what is the measure of angle 3? why?
a. angle 3 is 117 degrees because angle 1 and angle 3 form a line.
b. angle 3 is 63 degrees because angle 1 and angle 3 are vertical angles.
c. Angle 3 is 63 degrees because angle 1 and angle 3 are corresponding angles.
d. There is not enough information in the figure to establish this
d. There is not enough information in the figure to establish this.
d. There is not enough information in the figure to establish the measure of angle 3.
To find the measure of angle 3, we need to consider the relationship between angle 1 and angle 3 in the given picture. Let's analyze the answer choices one by one:
a. Angle 3 is 117 degrees because angle 1 and angle 3 form a line.
This answer choice suggests that angle 1 and angle 3 are supplementary angles, meaning they add up to 180 degrees because they form a straight line. However, there is no information in the question to support this claim. Therefore, we can eliminate this option.
b. Angle 3 is 63 degrees because angle 1 and angle 3 are vertical angles.
This answer choice states that angle 3 is equal to angle 1 because they are vertical angles, which are formed by intersecting lines. Vertical angles are always congruent, meaning they have the same measure. Therefore, if angle 1 is 63 degrees, then angle 3 must also be 63 degrees, making this option a possible correct answer.
c. Angle 3 is 63 degrees because angle 1 and angle 3 are corresponding angles.
This answer choice suggests that angle 3 is equal to angle 1 because they are corresponding angles. However, corresponding angles are only congruent when the lines being intersected are parallel. Without any information about parallel lines in the figure, we cannot assume that angle 3 is 63 degrees based on this reasoning. Hence, this option can be eliminated.
d. There is not enough information in the figure to establish this.
This answer choice suggests that we cannot determine the measure of angle 3 based on the given figure. It implies that we do not have enough information to make any conclusions about angle 3. This option is a valid choice if there is no other information provided in the question, which would make it impossible to determine the measure of angle 3.
Based on the analysis, the correct answer is either (b) Angle 3 is 63 degrees because angle 1 and angle 3 are vertical angles if the question provides no further context or (d) There is not enough information in the figure to establish this if additional information is not given.