express 40% of right angle into radian measure.
express two third of straight angle into radian.
express sum of angles of a quadrilateral intoradian.
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Why did the angle feel so rad? Because it's about to rock out in radians!
To express 40% of a right angle (90 degrees) in radian measure, we can use the conversion formula: 1 radian = 180/π degrees. So, 40% of a right angle is equal to 40% of 90 degrees, or 0.40 * 90 degrees. Converting this into radians, we have:
0.40 * 90 degrees * (π radians / 180 degrees) = 0.20π radians
Thus, 40% of a right angle is equal to 0.20π radians.
Now, let's tackle two thirds of a straight angle (180 degrees). This is like a fraction party! Two-thirds of a straight angle is equal to (2/3) * 180 degrees. Converting this to radians:
(2/3) * 180 degrees * (π radians / 180 degrees) = (2/3)π radians
So, two thirds of a straight angle is equal to (2/3)π radians.
Finally, let's find the sum of angles in a quadrilateral in radians. A quadrilateral has four angles, and their sum is always equal to 360 degrees. Converting this into radians:
360 degrees * (π radians / 180 degrees) = 2π radians
Therefore, the sum of angles in a quadrilateral is equal to 2π radians. A whole lot of radian fun!
To express a percentage of a right angle in radians, you need to determine what fraction of the full angle (which in this case is 90 degrees) the given percentage represents, and then convert it to radians. Here's how you can do it:
1. Determine the fraction: 40% of a right angle can be expressed as 40/100 or 2/5.
2. Convert the fraction to radians: To convert a fraction of an angle to radians, multiply the fraction by the conversion factor (π/180), where π represents pi (approximately 3.14159) and 180 represents the measure of a full angle in degrees.
- For 40% of a right angle: (2/5) * (π/180) = (2π/900) radians.
Therefore, 40% of a right angle is equal to (2π/900) radians.
To express two-thirds of a straight angle in radians, follow the same steps:
1. Determine the fraction: Two-thirds of a straight angle can be expressed as 2/3.
2. Convert the fraction to radians: Multiply the fraction by the conversion factor (π/180).
- For two-thirds of a straight angle: (2/3) * (π/180) = (2π/270) radians.
Therefore, two-thirds of a straight angle is equal to (2π/270) radians.
For the sum of angles in a quadrilateral, you need to consider that a quadrilateral has four angles in total. The sum of all the angles in a quadrilateral is always equal to 360 degrees or 2π radians.
Therefore, the sum of angles in a quadrilateral is equal to 2π radians.
a right angle is π/2 radians
I expect that by now you know how to handle fractions, and how the angles of a quadrilateral add up.