Answer:
[tex]B = 134^o[/tex]
Step-by-step explanation:
[tex]n = 6[/tex] --- sides
[tex]A = 170^o[/tex]
[tex]C = 107^o[/tex]
[tex]D = 102^o[/tex]
[tex]E = 117^o[/tex]
[tex]F = 90^o[/tex]
Required
The measure of B
The interior angles of a polygon is:
[tex]Angles = (n - 2) * 180[/tex]
So, we have:
[tex]Angles = (6 - 2) * 180[/tex]
[tex]Angles = 4 * 180[/tex]
[tex]Angles = 720^o[/tex]
The measure of B is calculated using:
[tex]A + B + C + D + E + F = 720[/tex]
Substitute known values
[tex]107 + B + 170 + 102 + 117 + 90 = 720[/tex]
Collect like terms
[tex]B + 107 + 170 + 102 + 117 + 90 = 720[/tex]
[tex]B + 586 = 720[/tex]
Collect like terms
[tex]B = 720 - 586[/tex]
[tex]B = 134^o[/tex]
