Answer:
m<VXZ = 56°
Step-by-step explanation:
Given that these lines are midpoints, they must be parrallel from each other which means that the corresponding angles are congruent.
Therefore the following equation is true:
m<YZW = m<VXZ
______________
Since we now have this equation, substitute the expressions of the angles into the equation.
m<YZW = m<VXZ
| |
v v
92 - 9x = 64 - 2x
+9x +9x
92 = 7x + 64
-64 -64
28 = 7x
÷7 ÷7
4 = x
_____
x = 4
____
Now since we know x is 4, substitute this back into the expressions given to find both of their measures.
x = 4 → 92 - 9x = 64 - 2x
92 - 9(4) = 64 - 2(4)
92 - 36 = 64 - 8
56 = 56 [these are the measures of both angles]
Therefore: m<VXZ = 56°
