Problem $1$

A zenith angle was measured six times with both faces of a total station. The average direct

reading is $86{34}^{\text{'}}{31}^{\text{'}\text{'}}$ with a standard deviation of $+-{12\mathrm{.}8}^{\text{'}\text{'}}.$ With the reverse face, it was

observed as $273{25}^{\text{'}}{12}^{\text{'}\text{'}}$ with a standard deviation of $+-{8\mathrm{.}8}^{\text{'}\text{'}}.$ What is the most probable value

for the zenith angle in the direct face?