Angles in a transversal can be congruent either by theorems of corresponding and vertical angles.
The measure of the angles are:
[tex]\angle 1 = 97^o[/tex]
[tex]\angle 2 = 83[/tex]
[tex]\angle 3 = 66[/tex]
[tex]\angle 4 = 114^o[/tex]
[tex]\angle 5 = 83^o[/tex]
[tex]\angle 6 = 97^o[/tex]
[tex]\angle 7 = 114^o[/tex]
[tex]\angle 8 = 66^o[/tex]
[tex]\angle 9 = 97^o[/tex]
[tex]\angle 10 = 83[/tex]
[tex]\angle 11 = 66[/tex]
[tex]\angle 12 = 114^o[/tex]
[tex]\angle 13 = 83^o[/tex]
[tex]\angle 14 = 97^o[/tex]
[tex]\angle 15 = 114^o[/tex]
[tex]\angle 16 = 66^o[/tex]
Given that:
[tex]\angle 9 = 97^o[/tex]
[tex]\angle 12 = 114^o[/tex]
The following angles are congruent by theorem of vertical angles.
[tex]\angle 9[/tex] and [tex]\angle 14[/tex]
[tex]\angle 12[/tex] and [tex]\angle 15[/tex]
So, we have:
[tex]\angle 14 = 97^o[/tex]
[tex]\angle 15 = 114^o[/tex]
Apply the theorem of angles on a straight line, we have:
[tex]\angle 9 + \angle 10 = 180[/tex]
[tex]\angle 11 + \angle 12 = 180[/tex]
So, we have:
[tex]\angle 10 = 180 - 97[/tex]
[tex]\angle 10 = 83[/tex]
[tex]\angle 11 = 180 - 114[/tex]
[tex]\angle 11 = 66[/tex]
The following angles are congruent by theorem of vertical angles.
[tex]\angle 10[/tex] and [tex]\angle 13[/tex]
[tex]\angle 11[/tex] and [tex]\angle 16[/tex]
So, we have:
[tex]\angle 13 = 83^o[/tex]
[tex]\angle 16 = 66^o[/tex]
The following angles are congruent by theorem of corresponding angles.
[tex]\angle 9[/tex] and [tex]\angle 1[/tex] [tex]\angle 13[/tex] and [tex]\angle 5[/tex] [tex]\angle 10[/tex] and [tex]\angle 2[/tex]
[tex]\angle 14[/tex] and [tex]\angle 6[/tex] [tex]\angle 11[/tex] and [tex]\angle 3[/tex] [tex]\angle 15[/tex] and [tex]\angle 7[/tex]
[tex]\angle 12[/tex] and [tex]\angle 4[/tex] [tex]\angle 16[/tex] and [tex]\angle 8[/tex]
So, we have:
[tex]\angle 1 = 97^o[/tex]
[tex]\angle 4 = 114^o[/tex]
[tex]\angle 6 = 97^o[/tex]
[tex]\angle 7 = 114^o[/tex]
[tex]\angle 2 = 83[/tex]
[tex]\angle 3 = 66[/tex]
[tex]\angle 5 = 83^o[/tex]
[tex]\angle 8 = 66^o[/tex]
Read more about corresponding and vertical angles at:
https://brainly.com/question/14209455
