To find the measures of angles 1, 2, and 3, we will use the information provided along with the relationships among the angles.
Given:
- \( \text{m}\angle 1 = 75^\circ \)
- \( \text{m}\angle 2 = 30^\circ \)
- \( \text{m}\angle 3 = 40^\circ \)
Based on the hint provided, we start by confirming the measures of the angles in the context of their positions and relationships.
Finding the Measures of Angles:
-
Calculate m∠1:
- The measure of angle 1 is given as \( 75^\circ \).
-
Calculate m∠2:
- The measure of angle 2 is given as \( 30^\circ \).
-
Calculate m∠3:
- The measure of angle 3 is given as \( 40^\circ \).
Summary of Angle Measures:
- \( m\angle 1 = 75^\circ \)
- \( m\angle 2 = 30^\circ \)
- \( m\angle 3 = 40^\circ \)
These angles can also be verified based on their relationships with each other. If they are part of a triangle, their sum should be equal to \( 180^\circ \). If they are supplementary or complementary to any other angles, those relationships should also be checked.
Example of verification if they form a triangle: \[ m\angle 1 + m\angle 2 + m\angle 3 = 75^\circ + 30^\circ + 40^\circ = 145^\circ \] This indicates that they do not form a triangle since the sum is less than \( 180^\circ \). You may need additional information if they are part of a different geometric figure.
If you're working with specific geometric relationships, or if there are additional angles or relationships that come into play, please provide that context for a more detailed solution!