An angle is 20 degrees less than thrice it's supplement. Find the measures of these angles
X+20=3 (180-x)
X+20=540-3x
X+3x=540-20
4x=520
X=520/4
X=130
Let's denote the measure of the angle as x.
The supplement of an angle is the angle that, when added to the given angle, results in a straight angle, which measures 180 degrees.
So, the supplement of the angle can be expressed as (180 - x).
According to the problem, the given angle is 20 degrees less than three times its supplement, which can be represented as:
x = 3(180 - x) - 20
Simplifying the equation:
x = 540 - 3x - 20
x + 3x = 540 - 20
4x = 520
x = 520/4
x = 130
Therefore, the measure of the angle is 130 degrees, and its supplement is (180 - 130) = 50 degrees.
To solve this problem, let's start by defining the unknown angles.
Let's say the angle we are trying to find is "x" degrees.
According to the problem, this angle is 20 degrees less than three times its supplement.
The supplement of an angle is the angle that, when added to the given angle, forms a straight angle of 180 degrees.
So, the supplement of angle "x" is 180 - x degrees.
Now, let's use the given information to form an equation and solve for "x".
According to the problem, the angle "x" is 20 degrees less than thrice its supplement.
This can be written as:
x = 3(180 - x) - 20
Let's solve this equation step by step:
x = 3(180 - x) - 20
x = 540 - 3x - 20
x + 3x = 540 - 20
4x = 520
x = 520 / 4
x = 130
Therefore, the angle x measures 130 degrees.
To find the supplement, we can substitute the value of x into the equation for the supplement:
Supplement of x = 180 - x
Supplement of x = 180 - 130
Supplement of x = 50
So, the supplement of angle x measures 50 degrees.
Therefore, the measures of the angles are:
Angle x = 130 degrees
Supplement of x = 50 degrees
a + 20 = 3 (180-a)
a + 20 = 540 - 3 a
4 a = 520
a = 130
180-a = 50