Question

$\overline{\mathrm{MN}}$is the median of trapezoid$\mathbf{ZOID}$ .

If trapezoid$\mathbf{ZOID}$ is isosceles and$\mathbf{m}\angle \mathbf{D}\mathbf{=}\mathbf{80}$ , then $\mathbf{m}\angle O=\underset{\_}{?}$.

Short answer

If trapezoid$ZOID$ is isosceles and $m\angle D=80$, then $\mathbf{m}\angle \mathbf{O}\mathbf{=}\mathbf{100}$.

Step-by-step solution

­- Observe the given diagram.

The given diagram is:

- Description of step.

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

From the given diagram it can be noticed that the angles and are the base angles of isosceles trapezoid.

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

Therefore,$\angle D\cong \angle I$ .

Therefore,$\angle D=\angle I=80°$ .

- Description of step.

As, the trapezoidZOID has parallel sides asZ0 and DL.

As,$ZO\parallel DI$ and OI is a transversal, therefore the angles $\angle O$and$\angle I$ are the adjacent angles on the same side of transversal.

As, the sum of the adjacent angles is , therefore the sum of the angles$\angle O$ and$\angle I$ is180 .

Therefore, it can be obtained that:

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

Therefore, the measure of the angle0 is $100°$.

- Write the complete statement.

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