Answer:
In order to find the value of x, one must first find the value of the other to angles in the triangle in which the value of x resides in order to be able to use the triangle sum theorem, which states that the sum of the measure of the angles in a triangle is 180 degrees. To find the angle in the lower right of the triangle, one must use the linear pair theorem which states two angles that form a linear pair are supplementary, meaning that they add up to 180 degrees. This will then allow you to subtract 160 from 180 to get the value of the angle in the lower right of the triangle, 20 degrees. To find the angle in the lower left of the triangle one must use the congruent supplements theorem which states if two angles are supplements of the same angle, then they are congruent, or equal to one another. Since a and b are parallel to one another, this must mean that the 60 degrees in the top left and the degree in the lower left of the triangle must be supplements of the same angle, and are therefore congruent, meaning that it would be equal to 60 degrees. Then, by using the triangle sum theorem, subtracting 60 and 20 from 180 will grant the answer x = 100 degrees, as is shown by the statement preceding the question.
Step-by-step explanation:
Sorry for the big wall of text but I didn't see any way to tone down the amount of words.
Anyways I hope this helps and I apologize for the semi-late response.
