Use the image to answer the question.%0D%0A%0D%0A%0D%0A%0D%0AAngle 8 is 110°%0D%0A110%0D%0A°%0D%0A and lines P%0D%0A%0D%0A and Q%0D%0A%0D%0A are parallel. Find the measure of angle 2.%0D%0A%0D%0A(1 point)%0D%0A°
To find the measure of angle 2, we can use the property that alternate interior angles are congruent when two parallel lines are cut by a transversal.
Since angle 8 is 110°, angle 2 is the alternate interior angle. Therefore, the measure of angle 2 is also 110°.
In the image, we can see that angle 8 and angle 2 are corresponding angles because they are both on the same side of the transversal line P and Q, and they are formed by the parallel lines P and Q.
Therefore, angle 2 must be equal to angle 8 since corresponding angles are congruent.
Since angle 8 is given as 110°, angle 2 must also be 110°.
Therefore, the measure of angle 2 is 110°.
To find the measure of angle 2, we need to use the information given in the problem, along with the properties of parallel lines and transversals.
First, let's analyze the image and label the relevant angles:
```
|--------------------------|
| |
| 2 |
| |
___ | ---------- P -----------|____
\ \
\ \
\ \
\ 8 \
\ \
\ \
\ \
Q \ 110° \
\ \
\ 1 \
|---------- C ---------------------|
```
In the given problem, we are told that line P and line Q are parallel. Therefore, angles 8 and 2 are corresponding angles. Corresponding angles are equal when the lines being intersected by the transversal (line C) are parallel.
Since angle 8 is given as 110°, angle 2 will also be 110°.
Therefore, the measure of angle 2 is 110°.