Question

ind the measures of angles​ 1, 2, and 3.
​(Hint: Find mangle∠​1, then mangle∠​2, and then mangle∠​3.)
11
22
33
85 degrees85°
40 degrees40°
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 enter your response heredegrees°.
​(Simplify your answer. Type an integer or a​ decimal.)

Answer 1

To find the measures of angles 1, 2, and 3 based on your description, it seems we need to use the relationships between the angles.

Let's denote the three angles as follows:
- \( m\angle 1 = x \)
- \( m\angle 2 = 40^\circ \)
- \( m\angle 3 = 40^\circ \)

### Finding \( m\angle 1 \)
From the information provided:
- If \( \angle 1 \) is adjacent to \( \angle 2 \) and \( \angle 3 \) and forms a linear pair with one, we can sum angles around a point or along a line to find \( m\angle 1 \).

If \( \angle 1 \) is formed with the \( 85^\circ \) angle we need to consider if the provided \( 40^\circ \) angles are related to it. We can analyze based on the assumption that they probably form a triangle or are related in some manner.

Assuming \( \angle 1 \) and \( 40^\circ \) together with \( 85^\circ \) create an angle measure summing to \( 180^\circ \):
1. Calculate \( m\angle 1 \):

\[
m\angle 1 + 40^\circ + 85^\circ = 180^\circ
\]
\[
m\angle 1 + 125^\circ = 180^\circ
\]
\[
m\angle 1 = 180^\circ - 125^\circ
\]
\[
m\angle 1 = 55^\circ
\]

So, \( m\angle 1 = 55^\circ \).

### Finding \( m\angle 2 \)
Since \( m\angle 2 = 40^\circ \), this value is as given and does not need further calculations.

### Finding \( m\angle 3 \)
Similarly, since \( m\angle 3 = 40^\circ \), this value is also as given and does not need further calculations.

### Summary of measures
- \( m\angle 1 = 55^\circ \)
- \( m\angle 2 = 40^\circ \)
- \( m\angle 3 = 40^\circ \)

### Final Answers
The measure of angle 1 is **55 degrees**.
The measure of angle 2 is **40 degrees**.
The measure of angle 3 is **40 degrees**.