91Ó°ÊÓ

The provided diagram is,

The measurement of one angle in the diagram is$80°$. The numbered angles are 1, 2, 3, 4, 5, 6, 7 as given in the diagram.

The sum of the linear paired angles is $180°$, $80°+m∠1=180°$.

The measure of $∠1$ will be,

$\begin{array}{c}{80}^{∘}+m∠1={180}^{∘}\\ m∠1={180}^{∘}−{80}^{∘}\\ m∠1={100}^{∘}\end{array}$

Since vertically opposite angles are equal, $m∠1=m∠2$and $m∠3=80°$.

Therefore, $m∠2=100°$ and $m∠3=80°$.

From the given figure, $∠2$and $∠5$, and the angles $∠3$ and $∠4$ are two pairs of alternate interior angles.

Since alternate interior angles are equal, $m∠5=m∠2$and $m∠3=m∠4$.

Therefore, the measures of $∠4$ and $∠5$ will be,

$\begin{array}{l}m∠5=m∠2\\ m∠5=100°\\ \\ m∠4=m∠3\\ m∠4=80°\end{array}$

Since vertically opposite angles are equal, $m∠5=m∠6$and $m∠4=m∠7$.

Therefore, the measures of $∠4$ and $∠5$ will be,

$\begin{array}{l}m∠6=m∠5\\ m∠6=100°\\ \\ m∠7=m∠4\\ m∠7=80°\end{array}$

The measures of the numbered angles are $m∠1=100°$, $m∠2=100°$, $m∠3=80°$, $m∠4=80°$, $m∠5=100°$, $m∠6=100°$, and $m∠7=80°$.