have 2 || lines C and d. lines intersect lines are a and b. On a, has 2 alternate interior <s 95 and x; 2 al. exterior <s 95 and 85 degrees. On b, consecutive interior <s 72 and y. What is x and y. Please explain reasoning in paragraph proof.
To find the measures of angles x and y, we need to apply the properties of parallel lines and transversals.
Given:
- We have two parallel lines, C and D.
- There are two lines, A and B, that intersect C and D.
- On line A, we have two pairs of alternate interior angles: one pair measuring 95 degrees and another pair measuring x degrees.
- On line A, we also have two pairs of alternate exterior angles: one pair measuring 95 degrees and another pair measuring 85 degrees.
- On line B, we have a pair of consecutive interior angles measuring 72 degrees and y degrees.
We can begin by using the property of alternate interior angles formed by a transversal (line A) intersecting two parallel lines (C and D). Since the pair of alternate interior angles formed by lines A and C is given as 95 degrees, we know that the other pair of alternate interior angles formed by lines A and D must also measure 95 degrees. Therefore, we can conclude that angle x must be 95 degrees.
Next, we can apply the property of alternate exterior angles. The pair of alternate exterior angles formed by lines A and C is given as 95 degrees. According to the property of alternate exterior angles, the other pair of alternate exterior angles formed by lines A and D must also measure 95 degrees. However, in this case, we are given that the second pair of alternate exterior angles measures 85 degrees. This creates a contradiction since the measure of both pairs of alternate exterior angles should be the same. Therefore, this information is not consistent, and we cannot determine the exact measure of angle y.
In conclusion, we can determine that angle x measures 95 degrees, but we do not have enough information to determine the measure of angle y.