A decagon has 10 sides. One angle of a regular decagon measures (8w + 17)°. Determine the value of w. Round to the nearest whole number.
a) w = 144
b) w = 23
c) w = 16
d) w = 8
Since a decagon has 10 sides, it also has 10 angles.
In a regular decagon, all the angles are congruent.
Therefore, the measure of each angle is (10-2)*180°/10 = 144°.
Given that one angle measures (8w + 17)°, we can set up the equation:
(8w + 17)° = 144°
Subtracting 17° from both sides:
8w° = 127°
Dividing both sides by 8:
w = 15.875
Rounding to the nearest whole number, we get w = 16.
Therefore, the value of w is 16.
Answer: c) w = 16.