If an angle is 20 degrees less than thrice its supplement, find the ratio of the angle to its supplement. Thanks
A segment that is 150 cm long is divided into three parts in the ratio 2 : 3 : 5 : how long is each part?
x = 3(180-x)-20
x = 130
so, the ratio you want is 130/50
To solve this problem, let's start by defining the angle and its supplement.
Let the angle be represented by "x," and its supplement be represented by "180 - x" (since the sum of an angle and its supplement is always 180 degrees).
Now, we are given that the angle is 20 degrees less than three times its supplement. Mathematically, we can express this as:
x = 3(180 - x) - 20
Simplifying the equation:
x = 540 - 3x - 20
4x = 520
x = 520/4
x = 130
So, the angle is 130 degrees.
To find the ratio of the angle to its supplement, we divide the angle by its supplement:
Ratio = x / (180 - x)
Ratio = 130 / (180 - 130)
Ratio = 130 / 50
Ratio = 13 / 5
Therefore, the ratio of the angle to its supplement is 13/5.
To find the ratio of an angle to its supplement, we need to define the angle and its supplement using variables.
Let's call the angle "x" and its supplement "180 - x", since the supplement of an angle is equal to 180 degrees minus the angle.
Based on the given information, we can create an equation:
x = 3(180 - x) - 20
Now, let's solve the equation to find the value of x.
First, distribute 3 to both terms within the parentheses:
x = 540 - 3x - 20
Combine like terms:
x + 3x = 540 - 20
4x = 520
Divide both sides by 4:
x = 520/4
x = 130
So, the value of the angle "x" is 130 degrees.
To find the supplement of the angle, substitute the value of x into the equation for the supplement:
180 - x = 180 - 130 = 50
The supplement of the angle is 50 degrees.
Now, we can calculate the ratio of the angle to its supplement:
Ratio = Angle / Supplement = x / (180 - x)
Ratio = 130 / (180 - 130) = 130 / 50 = 13/5 or 2.6
Therefore, the ratio of the angle to its supplement is 13:5 or 2.6.