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

Find The Measure Of Each Angle And The Postulate Or Theorem That Justifies Your Answer Find Mlt2 Mlt3 Mlt4 Mlt5 class=

Sagot :

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

[tex]m\angle2=135º[/tex]

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:

[tex]m\angle4=135º[/tex]

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:

[tex]m\angle4+m\angle3=180[/tex]

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

[tex]\begin{gathered} 135+m\angle3=180 \\ \Rightarrow m\angle3=180-135 \\ \therefore m\angle3=45 \end{gathered}[/tex]

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

[tex]m\angle5=45º[/tex]

Therefore, the answers are:

[tex]\begin{gathered} m\angle2=135º \\ m\angle3=45º \\ m\angle4=135º \\ m\angle5=45º \end{gathered}[/tex]

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