Explanation:
When two parallel lines are cut by a transversal, the interior angles on the same side of the transversal are supplementary. This means that their measures add up to 180 degrees.
In this case, the two interior angles on the same side of the transversal 't' are (2x-8) degrees and (3x-7) degrees. Since these angles are supplementary, we can write the equation (2x-8) + (3x-7) = 180.
Solving this equation for x, we get:
(2x-8) + (3x-7) = 180
5x - 15 = 180
5x = 195
x = 39
Substituting this value of x into the expressions for the two interior angles, we find that their measures are:
(2x-8) = (2*39 - 8) = 70 degrees
(3x-7) = (3*39 - 7) = 110 degrees
So, the measure of each of these angles is 70 degrees and 110 degrees.