Use the diagram below to find the measured value of x.

They're the same angle. I would look up transversals so you could understand it a bit more. I'll upload a picture of a transversal in my answer but you should search it anyways.

Anyways,

To solve, you set 160 equal to the other side.

160 = 3x + 10

150 = 3x

x = 50

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.