Question

In the figure, m<2=92 and m<12=74. Find the measure of each angle. Tell which postulate (s) or theorem (s) you used.

Answer 1

Answer:

$\angle 10=92\°\\\angle 8 = 92\°\\\angle 9=88\°\\\angle 5=106\°\\\angle 11 = 106\°\\\angle 13 = 106\°$

Step-by-step explanation:

In the figure $m \parallel n$, and r and s are transversal that intercept those parallels.

Now, from the each interception of each transversal we have 8 angles related.

$\angle 1, \angle 2, \angle 7, \angle 8, \angle 9, \angle 10, \angle 16, \angle 15$, all these angles are related.

$\angle 3, \angle 4, \angle 5, \angle 6, \angle 11, \angle 12, \angle 13, \angle 14$, all these angles are related.

By corresponding angles, we have the following congruence

$\angle 2 \cong \angle 10$

This means that

$\angle 10 = \angle 2= 92\°$

$\angle 9 = 180\° - \angle 10$,  by supplementary angles.

$\angle 9= 180\°-92\°=88\°$

$\angle 8 = \angle 2$, by vertical angles theorem.

$\angle 8= 92$

$\angle 5 = \angle 11$, by alternate interior angles.

$\angle 11=180\° - \angle 12$, by supplementary angles.

$\angle 11= 180\°-74\°=106\°$

$\angle 5=106\°$

$\angle 13 = \angle 11$, by vertical angles theorem.

$\angle 13 = 106\°$

Therefore, the answers are

$\angle 10=92\°\\\angle 8 = 92\°\\\angle 9=88\°\\\angle 5=106\°\\\angle 11 = 106\°\\\angle 13 = 106\°$

Answer 2

Answer:

m∠10 = 92°

m∠8 = 92°

m∠9 = 88°

m∠5 = 88°

m∠11 = 88°

m∠13 = 88°

Step-by-step explanation:

m∠10 = 92° (corresponding angles are equal)

m∠8 = 92° (Vertically opposite angles are equal)

m∠9 = m∠7 = 88° (Alternate interior angles are equal)

m∠5 = m∠7 = 88°  (corresponding angles are equal)

m∠11 = m∠5 = 88°  (Alternate interior angles are equal)

m∠13 = m∠11 = 88° (vertically opposite angles are equal)