A road sign is in the shape of a regular pentagon. What are the measure of each angle on the sign

Pentagon has five sides
5-2=3
3times 180 is 540
540 is total angles
540 divided by 5 is 108

A triangle has 180° and a quadrilateral (4 sides) has 360°.  For each additional side we add 180° so a 5 sided figured has 360 + 180 = 540° total.  540/5 (5 sides) = 108° per angle.

Formula for any number of sides where s is the number of sides =  (s-2)180°    
Let’s try if for 3 sides  (3-2) 180 = 1 (180) = 180°
Now four sides  (4-2) 180 = 2(180) = 360°
And finally, your pentagon  = (5-2) 180 = 3(180) = 540°
and 540 shared equally in a regular pentagon (regular means all sides and angles are the same) means 108 degrees in each angle   540÷5 = 108°


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