The value of x in question 1 is 43°. The measure of angle x is -29 degrees and the measure of angle y is 209 degrees in question 2.
For question 1:
Lines a and b are parallel if the corresponding angles are equal or supplementary. In this case, we have:
48° + (3x + 3)° = 180° (supplementary angles)
Solving for x, we get:
3x = 129°
x = 43°
Therefore, the value of x is 43°.
For question 2:
Step 1: Find the measure of angle x.
We are given that the exterior angle of the triangle measures 141 degrees. We are also given that the interior angle opposite to side x measures 68 degrees. The sum of the interior angles of a triangle is 180 degrees, so we can find the measure of angle x by subtracting the measures of the other two angles from 180 degrees.
angle x = 180 degrees - 68 degrees - 141 degrees
angle x = -29 degrees
Step 2: Find the measure of angle y.
We are given that angle y is supplementary to angle x. Supplementary angles sum to 180 degrees.
angle y = 180 degrees - angle x
angle y = 180 degrees - (-29 degrees)
angle y = 209 degrees