express the angular measurement of angle of a regular decagon in degree grades and radian
To express the angular measurement of an angle in a regular decagon, we need to calculate the central angle formed by two adjacent sides.
Step 1: Determine the total number of sides in the regular decagon.
A regular decagon has 10 sides.
Step 2: Calculate the central angle formed by two adjacent sides.
To find the central angle of a regular polygon, we use the formula:
Central angle = 360 degrees / Number of sides
In this case, the central angle of a regular decagon is:
Central angle = 360 degrees / 10
Central angle = 36 degrees
Step 3: Convert the angular measurement to grades.
One grade is equal to 1/400th of a circle or 0.9 degrees.
To convert degrees to grades, we use the formula:
Grades = Degrees * (400 / 360)
In this case, the angle of the regular decagon in grades is:
Grades = 36 degrees * (400 / 360)
Grades = 40 grades
Therefore, the angular measurement of the angle in a regular decagon is 36 degrees, 40 grades.
Step 4: Convert the angular measurement to radians.
To convert degrees to radians, we use the formula:
Radian = Degrees * (π / 180)
In this case, the angle of the regular decagon in radians is:
Radian = 36 degrees * (π / 180)
Radian = 0.6283 radians (rounded to four decimal places)
Therefore, the angular measurement of the angle in a regular decagon is 36 degrees, 40 grades, and approximately 0.6283 radians.
To express the angular measurement of an angle in a regular decagon, we need to determine the value of the angle in degrees, grades, and radians.
A regular decagon has 10 sides, which means that it consists of 10 equal angles. To find the value of one angle in the decagon, we can use the formula:
Angle = (360 degrees) / (number of sides)
1. Degree Measurement:
Using the formula above, we can find the degree measurement of one angle in the regular decagon:
Angle = (360 degrees) / (10)
Angle = 36 degrees
Therefore, one angle in a regular decagon measures 36 degrees.
2. Grade Measurement:
To convert the degree measurement to grade, we need to recall that 1 grade is equal to 0.9 degrees.
Angle (in grades) = Angle (in degrees) * (1 grade / 0.9 degrees)
Angle (in grades) = 36 degrees * (1 grade / 0.9 degrees)
Angle (in grades) = 40 grades
So, one angle in a regular decagon measures 40 grades.
3. Radian Measurement:
To convert the degree measurement to radians, we need to use the conversion factor that 180 degrees is equal to π radians.
Angle (in radians) = Angle (in degrees) * (π radians / 180 degrees)
Angle (in radians) = 36 degrees * (π radians / 180 degrees)
Angle (in radians) ≈ 0.628 radians (rounded to three decimal places)
Therefore, one angle in a regular decagon measures approximately 0.628 radians.
ten sides?
going around the outside we have to turn right ten times
that means each time we turn right 36 degrees which is 360/10
that means the interior angle= 180 - 36 = 144 degrees
in radians this is pi - 2pi/10
= 5 pi/5 - pi/5 = 4 pi/5