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 is with 70° larger than the other one.
To find the measures of all angles formed by the parallel lines a and b and transversal line c, we need to apply the properties of parallel lines and transversals.
Let's start by labeling the angles formed by line c intersecting lines a and b.
Angle 1: This is the angle formed by the intersection of line c with line a on one side.
Angle 2: This is the angle formed by the intersection of line c with line a on the opposite side.
Angle 3: This is the angle formed by the intersection of line c with line b on the same side as angle 1.
Angle 4: This is the angle formed by the intersection of line c with line b on the opposite side of angle 1.
Given that one of the angles is 70° larger than the other, let's assume that Angle 2 is 70° larger than Angle 1.
Therefore, Angle 2 = Angle 1 + 70°.
Since lines a and b are parallel, Angle 1 and Angle 3 are corresponding angles. Corresponding angles are congruent, meaning they have the same measure.
So, Angle 1 = Angle 3.
Now, let's apply the properties of angles formed by a transversal and parallel lines:
1. Alternate Interior Angles: Angle 2 and Angle 4 are alternate interior angles. Alternate interior angles are congruent when lines a and b are parallel.
2. Co-interior Angles: Angle 1 and Angle 4 are co-interior angles. Co-interior angles are supplementary when lines a and b are parallel.
Using this information, we can find the measures of all angles:
Angle 1 = x
Angle 2 is 70° larger than Angle 1: Angle 2 = x + 70°
Angle 3 = x
Angle 4 is congruent to Angle 2: Angle 4 = x + 70°
Since Angle 1 and Angle 3 are congruent, we have the equation:
x = x
Now, using the properties mentioned earlier:
Angle 2 and Angle 4 are alternate interior angles: x + 70° = x
Simplifying the equation: 70° = 0 [This is not possible]
Therefore, the given condition of one angle being 70° larger than the other is not possible in this case.
recall what you know about
alternate/adjacent interior/exterior angles