Lines a and b are parallel. Line c is a transversal. Find the measures of all angles formed by a,b, and c, if: one of the angles has measure of 150°.
To find the measures of all angles formed by parallel lines and a transversal, we can use the properties of corresponding angles, alternate interior angles, and alternate exterior angles.
In this case, since one angle has a measure of 150°, we'll label it as angle x.
By the property of corresponding angles, the angle corresponding to x will also have a measure of 150°. Let's label it as angle y.
Since lines a and b are parallel, angle x and angle y are corresponding angles.
Now, let's find the measures of the remaining angles.
Using the property of alternate interior angles, the angles on the opposite side of the transversal (line c) but between lines a and b will have the same measure. Therefore, we can label the interior angle formed by line a and line c as angle z.
So, angle z = 150°.
By the property of alternate exterior angles, the angles on the opposite side of the transversal (line c) but outside lines a and b also have the same measure. Let's label the exterior angle formed by line a and line c as angle w.
Since angle z and angle w are alternate exterior angles, they will have the same measure. Therefore, angle w = angle z = 150°.
To summarize:
- Angle x = 150°
- Angle y = 150°
- Angle z = 150°
- Angle w = 150°
All the angles formed by lines a, b, and c have a measure of 150°.