Answers:
x = 4
z = 61
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Work Shown:
The left and right angles (119 and 9x+83) are vertical angles.
Therefore, they are congruent or equal angles.
9x+83 = 119
9x = 119-83 ..... subtract 83 from both sides
9x = 36
x = 36/9 .... divide both sides by 9
x = 4
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To find the value of z, we take advantage of the fact that angles 119 and z are supplementary. They add to 180 degrees.
z+119 = 180
z = 180-119 .... subtract 119 from both sides
z = 61