ind the measures of angles​ 1, 2, and 3.

​(Hint: Find mangle∠​1, then mangle∠​2, and then mangle∠​3.)
11
22
33
75 degrees75°
30 degrees30°
40 degrees40°

left parenthesis The figure is not to scale. right parenthesis(The figure is not to scale.)
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Part 1
The measure of angle 1 is 7575degrees°.
​(Simplify your answer. Type an integer or a​ decimal.)
Part 2
The measure of angle 2 is 105105degrees°.
​(Simplify your answer. Type an integer or a​ decimal.)
Part 3
The measure of angle 3 is enter your response heredegrees°.
​(Simplify your answer. Type an integer or a​ decimal.)

1 answer

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).