To determine the measure of angle 3 based on the information given about angle 1 (which is 63°), we first need to understand the relationship between the angles.
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If angle 1 and angle 3 are corresponding angles and they are formed by a transversal cutting through two parallel lines, then angle 3 would also be 63°.
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If angle 1 and angle 3 are vertical angles, they would also be equal, meaning angle 3 would be 63° as well.
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If angle 1 and angle 3 are supplementary angles (form a linear pair), then the measure of angle 3 would be 117° (180° - 63° = 117°).
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If the figure does not provide enough context to establish the relationship between angle 1 and angle 3, one could argue that there is not enough information to determine angle 3.
Without the actual image or additional details about the orientation of the lines and how the angles are situated in relation to each other, it is difficult to definitively conclude the measure of angle 3.
However, based on the possible given responses, the correct answer would be dependent on the relationship defined in the figure. If angle 1 and angle 3 are either corresponding or vertical angles, angle 3 would be 63°. If they are supplementary, angle 3 would be 117°. Therefore, if the snippet states only the measure of angle 1 and does not clarify the relationship, the preferred answer would be that there is not enough information to establish this confidently.
If the figure clearly indicates the relationships (e.g., parallel lines and a transversal), you would choose the corresponding or vertical angles response accordingly.