Given the regular decagon, what is the measure of each numbered angle?
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a. m∡1 = 72°; m∡2 = 18°; m∡3 = 36°
b. m∡1 = 18°; m∡2 = 36°; m∡3 = 72°
c. m∡1 = 36°; m∡2 = 72°; m∡3 = 18°
d. m∡1 = 36°; m∡2 = 18°; m∡3 = 72°
c. m∡1 = 36°; m∡2 = 72°; m∡3 = 18°
In a regular decagon, each angle measures (n-2) x 180° / n, where n is the number of sides, which in this case is 10.
So, each angle measures (10-2) x 180° / 10 = 144° / 10 = 14.4°
Angle 1 is the first angle, so it measures 1 x 14.4° = 14.4°
Angle 2 is the third angle, so it measures 3 x 14.4° = 43.2°
Angle 3 is the fifth angle, so it measures 5 x 14.4° = 72°
Therefore, the answer is c. m∡1 = 36°; m∡2 = 72°; m∡3 = 18°.
The correct answer is c. m∡1 = 36°; m∡2 = 72°; m∡3 = 18°.
In a regular decagon, all angles have equal measures since it is a regular polygon. Since a decagon has 10 sides, the sum of the angles of a decagon can be calculated using the formula (n-2) * 180°, where n is the number of sides. Therefore, the sum of the angles of a decagon is (10-2) * 180° = 8 * 180° = 1440°.
To find the measure of each angle, we divide the sum of the angles by the number of angles, which is 10. So, each angle in a regular decagon measures 1440° / 10 = 144°.
In this case, m∡1 is labeled as 36°. However, since all angles in a regular decagon have equal measures, this is not possible. Therefore, options a, b, and d are incorrect.
The correct answer is c, where m∡1 is labeled as 36°, m∡2 is labeled as 72°, and m∡3 is labeled as 18°.