Answer:
72.5 & 35
Explanation:
If the difference between two same-side interior angles of two parallel lines is 35 degrees, we can determine the measures of the angles by using the properties of parallel lines and angles.
When two parallel lines are intersected by a transversal, such as a line that crosses both lines, the same-side interior angles are supplementary, meaning their measures add up to 180 degrees.
Let's denote one of the angles as x. The other angle can be expressed as (x + 35), as the given difference is 35 degrees.
Since the angles are supplementary, we can set up the equation:
x + (x + 35) = 180
Simplifying the equation:
2x + 35 = 180
Subtracting 35 from both sides:
2x = 145
Dividing both sides by 2:
x = 72.5
Therefore, one angle measures 72.5 degrees, and the other angle (x + 35) measures:
72.5 + 35 = 107.5 degrees.
Hence, the measures of the two angles are 72.5 degrees and 107.5 degrees.