Final answer:
To find the value of y for the angles of a hexagon, we calculate the sum of the interior angles and set up an equation using the given angle expressions. Solving this equation, we find that y equals 91 degrees.
Step-by-step explanation:
The total sum of the interior angles of a hexagon is calculated using the formula (n-2)×180°, where n is the number of sides. For a hexagon, n=6. Thus, the sum is: (6-2)×180° = 720°. The angles of the given hexagon are expressed in terms of y, so adding them together gives:
y + (y+15) + (y+25) + (y+35) + (y+45) + (y+54) = 720
Combining like terms, we have:
6y + 174 = 720
Subtracting 174 from both sides yields:
6y = 546
Dividing by 6 gives:
y = 91
Therefore, the measure of the smallest angle is 91 degrees.