Question

Find the measure of each angle and the Postulate or Theorem that justifies your answer. Find m<2, m<3, m<4, m<5

Answer 1

Notice that the angle 2 and that of 135º are vertical angles. Since vertical angles are congruent, they have the same measure. Then:

$m\angle2=135º$

Notice that the angles 2 and 4 are alternate interior angles. Alternate interior angles are congruent. Then, the measure of 4 is the same as the measure of 2:

$m\angle4=135º$

The angles 3 and 4 are adjacent and form a straight line. Therefore, those angles are supplementary angles, then, their measures must add up to 180º:

$m\angle4+m\angle3=180$

Since the measure of the angle 4 is 135º, then:

$\begin{gathered} 135+m\angle3=180 \\ \Rightarrow m\angle3=180-135 \\ \therefore m\angle3=45 \end{gathered}$

Finally, notice that the angles 3 and 5 are also vertical angles, so they have the same measure:

$m\angle5=45º$

Therefore, the answers are:

$\begin{gathered} m\angle2=135º \\ m\angle3=45º \\ m\angle4=135º \\ m\angle5=45º \end{gathered}$