Answer:
Angle 1 = 115 degrees
Angle 2 = 65 degrees
Explanation:
Angle 1: Same-side interior angle of Line 1
Angle 2: Same-side interior angle of Line 2
We know that the difference between the angles is 50 degrees. Since the angles are supplementary, we can write the equation:
Angle 1 + Angle 2 = 180
Now, we need to express the difference between the angles in terms of Angle 1 or Angle 2. We can choose either angle, so let's express it in terms of Angle 1:
Angle 1 - Angle 2 = 50
We can rewrite this equation as:
Angle 1 = 50 + Angle 2
Now substitute this expression for Angle 1 into the first equation:
(50 + Angle 2) + Angle 2 = 180
Combine like terms:
2Angle 2 + 50 = 180
Subtract 50 from both sides:
2Angle 2 = 130
Divide by 2:
Angle 2 = 65
Now substitute this value back into the equation for Angle 1:
Angle 1 = 50 + Angle 2
Angle 1 = 50 + 65
Angle 1 = 115
Therefore, the angles are as follows:
Angle 1 = 115 degrees
Angle 2 = 65 degrees