To solve for the measures of angles 1, 2, and 3, let’s derive values step by step as per the hints provided.
Part 1: Finding the measure of angle 1
You've already stated that the measure of angle 1 is 75 degrees.
Part 2: Finding the measure of angle 2
To find the measure of angle 2, we generally use the fact that the sum of angles around a point is 360 degrees or that angles on a straight line sum up to 180 degrees, depending on the configuration.
Since the measure of angle 1 is known, and assuming angle 2 is supplementary to some combination of the given angles, you can find angle 2.
From your provided value, the measure of angle 2 is 105 degrees.
Part 3: Finding the measure of angle 3
To find angle 3, we would typically look at any remaining angles or relationships between them. If angles 1 and 2 contribute to or relate directly to angle 3 through linear pairs, vertical angles, corresponding angles, etc., we can find angle 3 using those properties.
Assuming the standard relationship for angles in a triangle (if angles 1, 2, and 3 form a triangle), you could potentially set them together this way:
If angle 1 is 75° and angle 2 is 105°, we find angle 3 using the formula:
\[ m\angle 3 = 180 - (m\angle 1 + m\angle 2) \]
Substituting the values, we find:
\[ m\angle 3 = 180 - (75 + 105) \]
\[ m\angle 3 = 180 - 180 \]
\[ m\angle 3 = 0 , degrees \]
However, if the angles do not form a triangle and correlate to a shape or configuration given, you'll want to consider whatever applicable geometric rule provides context for angle 3.
Given what you've specified, please clarify or if angle 3 is simply reflective of parts defined by angle 1 or 2 directly.
If the correct answer comes from your find using geometrical properties based on figures likely shown to you (like supplementary or opposite angles), please provide that diagrammatically to derive a clearer angle 3.
If angle 3 connects to provided values, it might alternatively yield a deduced or supplemented relationship with the other angles.
So as per your calculation intents, based on your provided numbers:
- The measure of angle 1: 75 degrees
- The measure of angle 2: 105 degrees
- The measure of angle 3: 0 degrees (or as geometrically specified in your context).