Angle 8 is 110°
and lines P
and Q
are parallel. Find the measure of angle 2.
60
70
50
10
Unfortunately, without a visual diagram or additional description of how angles 2 and 8 relate to lines P and Q, as well as their positions (such as alternate interior angles, corresponding angles, vertical angles, etc.), it's not possible to provide a correct answer.
In the case of parallel lines cut by a transversal, the following angle relationships hold true:
1. Corresponding angles are equal.
2. Alternate interior angles are equal.
3. Alternate exterior angles are equal.
4. Consecutive interior angles (also known as same side interior angles) sum to 180 degrees.
If angle 8 is an exterior angle and angle 2 is its corresponding interior angle on the opposite parallel line, then angle 2 would also be 110 degrees due to the corresponding angles postulate.
If angle 8 is one of a pair of consecutive interior angles with respect to angle 2, then angle 2 would be 70 degrees, since 110 + 70 = 180 degrees.
If angle 8 is an alternate exterior angle with respect to angle 2 (assuming angle 2 is interior), then angle 2 would still be 110 degrees due to the alternate exterior angles theorem.
If angle 8 is an alternate interior angle with respect to angle 2 which is also interior, then angle 2 would again be 110 degrees due to the alternate interior angles theorem.
Without the specific layout, it is not possible to definitively state the measure of angle 2. Please provide additional information about the placement of the angles with respect to the parallel lines for an accurate answer.