Hello, juvenilepunk!
26. If two opposite angles of a quadrilateral measure 120°,
and the measure of the other angles are multiples of 10°,
what is the probability that the quadrilateral is a parallelogram?
The four interior angles of a quadrilateral add up to 360°.
Since $\displaystyle \angle A = \angle C = 120^o$, then: .$\displaystyle \angle B + \angle D \:=\:120^o$
Since $\displaystyle \angle B\text{ and }\angle D$ are multiples of 10°, there are 11 cases.
. . $\displaystyle \begin{array}{c|c} B & D \\ \hline
10 & 110 \\ 20 & 100 \\ 30 & 90 \\ 40 & 80 \\ 50 & 70 \\ {\color{blue}60} & {\color{blue}60} \\ 70 & 50 \\ 80 & 40 \end{array}$
. . $\displaystyle \begin{array}{c|c} 90 & \;30 \\ 100 & \;20 \\ 110 & \;10 \end{array}$
In only one case the quadrilateral is a parallelogram.
Code:
A * - - - - - - - - - * B
/ 120° 60° /
/ /
/ /
/ /
/ 60° 120° /
D * - - - - - - - - - * C
Therefore: .$\displaystyle P(\text{parallelogram}) \;=\;\frac{1}{11}$