The measures in this problem are given as follows:
1. x = 14.
2. m < 1 = 58º.
3. m < 2 = 122º.
How to obtain the measures?
Angles 1 and 2 are supplementary, as the angle 1 and the consecutive interior angle with angle 2 are corresponding angles, meaning that they are congruent, and then the angles are supplementary with their consecutive interior angles.
When two angles are supplementary, the sum of their measures is of 180º, hence the measure of x is obtained as follows:
m < 1 + m < 2 = 180
2x + 30 + 8x + 10 = 180
10x + 40 = 180
10x = 140
x = 140/10
x = 14.
Then the angle measures are obtained as follows:
- m < 1 = 2(14) + 30 = 58º.
- m < 2 = 8(14) + 10 = 122º.
More can be learned about parallel and transversal lines at https://brainly.com/question/24607467
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