Answer:
[tex]m \angle A = 100 \degree[/tex]
Step-by-step explanation:
Given:
[tex]m \angle A= (x-60) \degree \\ m \angle B= (x-40) \degree \\ m \angle C= 130\degree \\ m \angle D= 120\degree \\ m \angle E= 110\degree \\ m \angle F= (x-20) \degree[/tex]
Also, the given diagram is a perfect hexagon, having sum of all interior angles 720°
To find:
[tex]m \angle A= ?[/tex]
Solution:
[tex] \sf \: Sum \: of \: all \: interior \: angles = 720 \degree \\ \sf \: m \angle A + m \angle B + m \angle C + m \angle D + m \angle E + m \angle F = 720 \degree\\ \sf \: (x - 60) + (x - 40) +130 + 120 + 110 + (x - 20) = 720 \degree \\ \sf \: 3x - 120 + 120 + 240 = 720 \\ \sf 3x - \cancel{120}+ \cancel{120} + 240 = 720 \\ \sf 3x = 720 - 240 \\ \sf 3x = 480 \\ \sf x = \frac{480}{3} \\ \fbox{\sf x = 160 \degree}[/tex]
Substituting the value of x in,
[tex]m \angle A= (x-60) \degree \\ m \angle A= 160-60 \\ m \angle A = 100 \degree[/tex]
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