A triangle is a plane figure which has three sides and angles. Thus the sum of internal angles of a triangle is [tex]180^{o}[/tex]. Thus the answers to the missing values are:
7. x = [tex]108^{o}[/tex]
8. x = [tex]133^{o}[/tex]
9. x = [tex]124^{o}[/tex]
10. x = [tex]62^{o}[/tex]
11. x = [tex]74^{o}[/tex]
12. x = [tex]77^{o}[/tex]
13. a = [tex]35^{o}[/tex]
14. b = [tex]74^{o}[/tex]
15. c = [tex]66^{o}[/tex]
The sum of the internal angles of a triangle is [tex]180^{o}[/tex]. Thus in a given question, the required value for each missing value is:
7. Let the unknown inter nal angle ne represented by r, so that;
70 + 38 + r = [tex]180^{o}[/tex]
r = [tex]180^{o}[/tex] - 108
r = 72
So that,
x + a = [tex]180^{o}[/tex] (sum of angles on a staight line)
72 + a = [tex]180^{o}[/tex]
a = [tex]180^{o}[/tex] - 72
= [tex]108^{o}[/tex]
a = [tex]108^{o}[/tex]
8. x = 39 + 94 (Sum of two opposite interior angles is equal to an exterior angle)
x = [tex]133^{o}[/tex]
9. x = 43 + 81 (Sum of two opposite interior angles is equal to an exterior angle)
x = [tex]124^{o}[/tex]
10. x + 19 = 81 (Sum of two opposite interior angles is equal to an exterior angle)
x = 81 - 19
x = [tex]62^{o}[/tex]
11. 41 + x = 115 (Sum of two opposite interior angles is equal to an exterior angle)
x = 115 - 41
x = [tex]74^{o}[/tex]
12. x = 41 + 36 (Sum of two opposite interior angles is equal to an exterior angle)
x = [tex]77^{o}[/tex]
13. 33 + 112 + a = [tex]180^{o}[/tex] (sum of angles on a staight line)
a = [tex]180^{o}[/tex] - 145
= [tex]35^{o}[/tex]
14. b + 71 + a = [tex]180^{o}[/tex] (sum of angles on a staight line)
b = [tex]180^{o}[/tex] - 106
b = [tex]74^{o}[/tex]
15. c + 71 + 43 = [tex]180^{o}[/tex] (sum of angles on a staight line)
c = [tex]180^{o}[/tex] - 114
c = [tex]66^{o}[/tex]
For further clarifications on the sum internal angles of a triangle, visit: https://brainly.com/question/23327304
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