Angle 8 is 110°
and lines P
and Q
are parallel. Find the measure of angle 2.
(1 point)
Since lines P and Q are parallel, angle 8 is corresponding to angle 2 (alternate interior angles). Therefore, angle 2 must also be 110°.
To find the measure of angle 2, we first need to understand the relationship between angles formed by parallel lines.
When a transversal (a line that intersects two or more other lines) intersects two parallel lines, the corresponding angles are congruent.
In this case, angle 8 and angle 2 are corresponding angles, since they are in the same position relative to the parallel lines P and Q.
Since angle 8 measures 110°, we can conclude that angle 2 also measures 110°.
To find the measure of angle 2, we need to use the properties of parallel lines and their corresponding angles.
In this case, we have angle 8 as 110°, which is an exterior angle. The interior angles adjacent to angle 8 are angles 1 and 2.
The interior angles on the same side of the transversal (line P) and between the parallel lines (lines P and Q) are called "consecutive interior angles" and they are supplementary. In other words, the sum of angles 1 and 2 is equal to 180°.
Since angle 8 is 110°, we can find angle 1 by subtracting angle 8 from 180°:
angle 1 = 180° - angle 8
= 180° - 110°
= 70°
Now that we know angle 1 is 70°, we can find angle 2 by subtracting angle 1 from 180°:
angle 2 = 180° - angle 1
= 180° - 70°
= 110°
Therefore, the measure of angle 2 is 110°.