Final answer:
The measure of angle MXN is supplementary to angle YZX. The measure of angle LZX can be found using the cosine rule. The measure of angle MYL can be found using the sine rule.
Step-by-step explanation:
The measure of angle MXN in relation to angle YZX is that they are supplementary angles, which means that the sum of their measures is equal to 180 degrees. So, if angle YZX measures x degrees, then angle MXN measures 180 - x degrees.
The measure of angle LZX in relation to angles ZYX and YXZ can be determined using the cosine rule. The cosine rule states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the lengths of those two sides multiplied by the cosine of the included angle. So, we can use this formula to find the measure of angle LZX.
The measure of angle MYL in relation to angle ZYX can be found using the sine rule which states that in a triangle, the ratio of the length of a side to the sine of the opposite angle is constant. Using this rule, we can find the measure of angle MYL.