Given the regular decagon what is the measure of each numbered angle? There is a one in the first triangle, a three in the second, and a two in the sixth triangle in the decagon.
Here are the answer choices
m1=72, m2=18, m3=36
m1=18, m2=36, m3=72
m1=36, m2=72, m3=18
m1=36, m2=18, m3=72
answer c
To find the measure of each numbered angle in a regular decagon, we need to first determine the total measure of all the angles in the decagon.
A regular decagon has 10 sides, so the sum of all the interior angles in a decagon can be found using the formula:
Sum of interior angles = (n-2) * 180°
where n is the number of sides in the polygon. In this case, n = 10, so:
Sum of interior angles = (10-2) * 180°
= 8 * 180°
= 1440°
Since all the angles in a regular decagon are congruent (i.e., they have the same measure), we can divide the sum of interior angles by the number of angles to find the measure of each angle.
Measure of each angle = Sum of interior angles / Number of angles
= 1440° / 10
= 144°
Now, let's consider the given information about the numbered angles. In the first triangle, there is a "one" angle. This means that the angle with a measure of 72 degrees is the first angle (m1 = 72°).
In the second triangle, there is a "three" angle. This means that the angle with a measure of 36 degrees is the second angle (m2 = 36°).
In the sixth triangle, there is a "two" angle. This means that the angle with a measure of 72 degrees is the sixth angle (m6 = 72°).
So, the correct answer choice is:
m1 = 72, m2 = 36, m3 = 72