Answer:
(a) x = [tex]128^{o}[/tex]
(b) x = [tex]74^{o}[/tex]
Step-by-step explanation:
A. sum of angles in a polygon = (n - 2) 180
The polygon given is an irregular pentagon, where n = 5
So that;
sum of angles in a pentagon = (5 - 2) 180
= 3 x 180
= [tex]540^{o}[/tex]
Thus,
x + 90 + 76 + 110 + 136 = [tex]540^{o}[/tex]
x + 412 = [tex]540^{o}[/tex]
x = [tex]540^{o}[/tex] - 412
x = [tex]128^{o}[/tex]
B. The polygon given is an irregular pentagon, where n = 5.
Let the supplementary angle with angle 38 be represented by y,
y + 38 = 180
y = 180 - 38
= [tex]142^{o}[/tex]
y = [tex]142^{o}[/tex]
Let the supplementary angle with x be represented by z, so that;
z + 72 + 120 + 100 + 142 = [tex]540^{o}[/tex]
z + 434 = [tex]540^{o}[/tex]
z = [tex]540^{o}[/tex] - 434
= [tex]106^{o}[/tex]
z = [tex]106^{o}[/tex]
But, x + z = [tex]180^{o}[/tex]
Then;
x + [tex]106^{o}[/tex] = [tex]180^{o}[/tex]
x = [tex]180^{o}[/tex] - [tex]106^{o}[/tex]
= [tex]74^{o}[/tex]
x = [tex]74^{o}[/tex]
