Question

The angles of a hexagon are: y degrees, (y+15) degrees, (y+25) degrees, (y+35) degrees, (y+45) degrees, and (y+54) degrees. Find y.

a) Angle Relationships in Polygons
b) Solving for Unknown Angles
c) Hexagon Angle Measures
d) Geometry of Polygon Angles

Answer 1

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.