91Ó°ÊÓ

The given diagram is:

The theorem 5-18 states that the base angles of an isosceles trapezoid are congruent.

From the given diagram it can be noticed that the angles $∠D$and $∠I$are the base angles of an isosceles trapezoid.

Therefore by using the theorem 5-18 it can be said that the angles $∠D$and $∠I$are congruent.

Therefore, $∠Dâ‰\dots ∠I$.

Therefore, $∠D=∠I=80°$.

As, the trapezoid $ZOID$has parallel sides as $ZO$and $DI$.

As, $ZOâˆ\yen DI$and $OI$is a transversal, therefore the angles $∠O$and $∠I$are the adjacent angles on the same side of transversal.

As, the sum of the adjacent angles is $180°$, therefore the sum of the angles $∠O$and $∠I$is $180°$.

Therefore, it can be obtained that:

$\begin{array}{c}∠O+∠I=180°\\ ∠O+80°=180°\\ ∠O=180°−80°\\ ∠O=100°\end{array}$

Therefore, the measure of the angle O is $100°$.

If trapezoid $ZOID$is isosceles and $m∠D=80$, then $m∠O=100$.